M2110 Linear Algebra and Geometry II

Faculty of Science
Spring 2025
Extent and Intensity
2/2/0. 4 credit(s) (příf plus uk k 1 zk 2 plus 1 > 4). Recommended Type of Completion: zk (examination). Other types of completion: z (credit).
In-person direct teaching
Teacher(s)
prof. RNDr. Jan Paseka, CSc. (lecturer)
doc. RNDr. Martin Čadek, CSc. (seminar tutor)
Mgr. Mária Šimková (seminar tutor)
Guaranteed by
doc. RNDr. Martin Čadek, CSc.
Department of Mathematics and Statistics – Departments – Faculty of Science
Supplier department: Department of Mathematics and Statistics – Departments – Faculty of Science
Prerequisites
M1110 Linear Algebra I || M1111 Linear Algebra I ||( FI:MB003 Linear Algebra and Geometry I )
Knowledege of basic notion of linear algebra is supposed.
Course Enrolment Limitations
The course is also offered to the students of the fields other than those the course is directly associated with.
fields of study / plans the course is directly associated with
there are 7 fields of study the course is directly associated with, display
Course objectives
The aim of this second course in linear algebra is to introduce other basic notions of linear algebra. Passing the course the students *will know affine spaces, bilinear and quadratic forms, eingenvalues and eigenvectors of linear operators, *they will be able to solve problems concerning the spaces with scalar product and properties of orthogonal and selfadjoint operators and *to find the Jordan canonical form.
Learning outcomes
Passing the course the students *will know affine spaces, bilinear and quadratic forms, eingenvalues and eigenvectors of linear operators, *they will be able to solve problems concerning the spaces with scalar product and properties of orthogonal and selfadjoint operators and *to find the Jordan canonical form.
Syllabus
  • Affine geometry: affine spaces and subspaces, affine geometry and affine mappings. Linear forms: dual space, dual basis, dual homomorphism. Bilinear and quadratic forms: definition, matrix with respect to given basis, diagonalization, signature. Euklidean geometry: orthogonal projection, distance and deviation of affine subspaces. Linear operators: invariant subspaces, eigenvalues and eigen vectors, charakteristic polynomial, algebraic and geometric multiplicity of eigenvalues, conditions for diagonalization. Linear models. Ortogonal and unitar operators: definition and basic properties, eigenvalues, geometric meaning. Self adjoint operators: adjoint operator, symmetric and hermitian matrices, spectral decomposition. Jordan canonical form: nilpotent endomorphisms, root subspaces, computations.
Literature
  • PAVOL, Zlatoš. Lineárna algebra a geometria (Linear algebra and geometry). Bratislava: Albert Marenčin PT, s.r.o., 2011, 741 pp. ISBN 978-80-8114-111-9. info
  • PASEKA, Jan and Pavol ZLATOŠ. Lineární algebra a geometrie I. Elportál. Brno: Masarykova univerzita, 2010. ISSN 1802-128X. URL info
  • Zlatoš P.: Lineárna algebra a geometria, připravovaná skripta MFF Univerzity Komenského v Bratislavě, elektronicky dostupné na http://www.math.muni.cz/pub/math/people/Paseka/lectures/LA/
  • Slovák, Jan. Lineární algebra. Učební texty. Brno:~Masarykova univerzita, 1998. 138. elektronicky dostupné na http://www.math.muni.cz/~slovak.
Teaching methods
Lectures and exercises (tutorials).
Assessment methods
Exam: written and oral. Requirements for the exam: to obtain 50% of points from 6 tests written during semester. Requirements: to manage the theory from the lecture, to be able to solve the problems similar to those from exercises
Language of instruction
Czech
Follow-Up Courses
Further comments (probably available only in Czech)
Information on completion of the course: ukončení zápočtem možné pouze rozhodnutím učitele
The course is taught annually.
The course is taught: every week.
Credit evaluation note: 2 kr. zápočet.
Listed among pre-requisites of other courses
Teacher's information
http://www.math.muni.cz/~cadek
The exam consists of three parts: 1. Semester-long component: You need to score at least 50% of the points in 6 short written tests. 2. Written exam during the exam period: The written exam consists of a numerical and a theoretical part. Students who pass both parts of the written exam proceed to the oral exam. 3. Oral exam: During the oral exam, you will be required to demonstrate understanding of the topics covered and the ability to illustrate the concepts and theorems with examples. Additional notes: The exam is designed to test your understanding of the material, not your ability to memorize definitions. You are encouraged to ask questions during lectures and tutorials if you do not understand something. There are many resources available to help you prepare for the exam, including the textbook, lecture notes, and online resources.
The course is also listed under the following terms Spring 2008 - for the purpose of the accreditation, Spring 2011 - only for the accreditation, Spring 2000, Spring 2001, Spring 2002, Spring 2003, Spring 2004, Spring 2005, Spring 2006, Spring 2007, Spring 2008, Spring 2009, Spring 2010, Spring 2011, Spring 2012, spring 2012 - acreditation, Spring 2013, Spring 2014, Spring 2015, Spring 2016, Spring 2017, spring 2018, Spring 2019, Spring 2020, Spring 2021, Spring 2022, Spring 2023, Spring 2024.

M2110 Linear Algebra and Geometry II

Faculty of Science
Spring 2024
Extent and Intensity
2/2/0. 4 credit(s) (příf plus uk k 1 zk 2 plus 1 > 4). Recommended Type of Completion: zk (examination). Other types of completion: z (credit).
Teacher(s)
prof. RNDr. Jan Paseka, CSc. (lecturer)
doc. RNDr. Martin Čadek, CSc. (seminar tutor)
Mgr. Mária Šimková (seminar tutor)
doc. PaedDr. RNDr. Stanislav Katina, Ph.D. (assistant)
doc. Mgr. Jan Koláček, Ph.D. (assistant)
Guaranteed by
prof. RNDr. Jan Paseka, CSc.
Department of Mathematics and Statistics – Departments – Faculty of Science
Supplier department: Department of Mathematics and Statistics – Departments – Faculty of Science
Timetable
Mon 19. 2. to Sun 26. 5. Wed 8:00–9:50 A,01026
  • Timetable of Seminar Groups:
M2110/01: Mon 19. 2. to Sun 26. 5. Mon 12:00–13:50 M5,01013, M. Čadek
M2110/02: Mon 19. 2. to Sun 26. 5. Mon 8:00–9:50 M2,01021, M. Čadek
M2110/03: Mon 19. 2. to Sun 26. 5. Mon 14:00–15:50 M2,01021, J. Paseka
M2110/04: Mon 19. 2. to Sun 26. 5. Tue 18:00–19:50 M1,01017, M. Šimková
Prerequisites
M1110 Linear Algebra I || M1111 Linear Algebra I ||( FI:MB003 Linear Algebra and Geometry I )
Knowledege of basic notion of linear algebra is supposed.
Course Enrolment Limitations
The course is also offered to the students of the fields other than those the course is directly associated with.
fields of study / plans the course is directly associated with
there are 7 fields of study the course is directly associated with, display
Course objectives
The aim of this second course in linear algebra is to introduce other basic notions of linear algebra. Passing the course the students *will know affine spaces, bilinear and quadratic forms, eingenvalues and eigenvectors of linear operators, *they will be able to solve problems concerning the spaces with scalar product and properties of orthogonal and selfadjoint operators and *to find the Jordan canonical form.
Learning outcomes
Passing the course the students *will know affine spaces, bilinear and quadratic forms, eingenvalues and eigenvectors of linear operators, *they will be able to solve problems concerning the spaces with scalar product and properties of orthogonal and selfadjoint operators and *to find the Jordan canonical form.
Syllabus
  • Affine geometry: affine spaces and subspaces, affine geometry and affine mappings. Linear forms: dual space, dual basis, dual homomorphism. Bilinear and quadratic forms: definition, matrix with respect to given basis, diagonalization, signature. Euklidean geometry: orthogonal projection, distance and deviation of affine subspaces. Linear operators: invariant subspaces, eigenvalues and eigen vectors, charakteristic polynomial, algebraic and geometric multiplicity of eigenvalues, conditions for diagonalization. Linear models. Ortogonal and unitar operators: definition and basic properties, eigenvalues, geometric meaning. Self adjoint operators: adjoint operator, symmetric and hermitian matrices, spectral decomposition. Jordan canonical form: nilpotent endomorphisms, root subspaces, computations.
Literature
  • Zlatoš P.: Lineárna algebra a geometria, připravovaná skripta MFF Univerzity Komenského v Bratislavě, elektronicky dostupné na http://www.math.muni.cz/pub/math/people/Paseka/lectures/LA/
  • Slovák, Jan. Lineární algebra. Učební texty. Brno:~Masarykova univerzita, 1998. 138. elektronicky dostupné na http://www.math.muni.cz/~slovak.
Teaching methods
Lectures and exercises (tutorials).
Assessment methods
Exam: written and oral. Requirements for the exam: to obtain 50% of points from 6 tests written during semester. Requirements: to manage the theory from the lecture, to be able to solve the problems similar to those from exercises
Language of instruction
Czech
Follow-Up Courses
Further comments (probably available only in Czech)
Study Materials
The course is taught annually.
Credit evaluation note: 2 kr. zápočet.
Listed among pre-requisites of other courses
Teacher's information
http://www.math.muni.cz/~cadek
The course is also listed under the following terms Spring 2008 - for the purpose of the accreditation, Spring 2011 - only for the accreditation, Spring 2000, Spring 2001, Spring 2002, Spring 2003, Spring 2004, Spring 2005, Spring 2006, Spring 2007, Spring 2008, Spring 2009, Spring 2010, Spring 2011, Spring 2012, spring 2012 - acreditation, Spring 2013, Spring 2014, Spring 2015, Spring 2016, Spring 2017, spring 2018, Spring 2019, Spring 2020, Spring 2021, Spring 2022, Spring 2023, Spring 2025.

M2110 Linear Algebra and Geometry II

Faculty of Science
Spring 2023
Extent and Intensity
2/2/0. 4 credit(s) (příf plus uk k 1 zk 2 plus 1 > 4). Recommended Type of Completion: zk (examination). Other types of completion: z (credit).
Teacher(s)
doc. RNDr. Martin Čadek, CSc. (lecturer)
prof. RNDr. Jan Paseka, CSc. (seminar tutor)
Mgr. Mária Šimková (seminar tutor)
doc. Mgr. Jan Koláček, Ph.D. (assistant)
doc. RNDr. Lenka Přibylová, Ph.D. (assistant)
Mgr. Richard Smolka (assistant)
Guaranteed by
doc. RNDr. Martin Čadek, CSc.
Department of Mathematics and Statistics – Departments – Faculty of Science
Supplier department: Department of Mathematics and Statistics – Departments – Faculty of Science
Timetable
Wed 12:00–13:50 A,01026
  • Timetable of Seminar Groups:
M2110/01: Tue 12:00–13:50 M2,01021, M. Čadek
M2110/02: Wed 14:00–15:50 M1,01017, M. Šimková
M2110/03: Mon 14:00–15:50 M1,01017, J. Paseka
Prerequisites
M1110 Linear Algebra I || M1111 Linear Algebra I ||( FI:MB003 Linear Algebra and Geometry I )
Knowledege of basic notion of linear algebra is supposed.
Course Enrolment Limitations
The course is also offered to the students of the fields other than those the course is directly associated with.
fields of study / plans the course is directly associated with
there are 7 fields of study the course is directly associated with, display
Course objectives
The aim of this second course in linear algebra is to introduce other basic notions of linear algebra. Passing the course the students *will know affine spaces, bilinear and quadratic forms, eingenvalues and eigenvectors of linear operators, *they will be able to solve problems concerning the spaces with scalar product and properties of orthogonal and selfadjoint operators and *to find the Jordan canonical form.
Learning outcomes
Passing the course the students *will know affine spaces, bilinear and quadratic forms, eingenvalues and eigenvectors of linear operators, *they will be able to solve problems concerning the spaces with scalar product and properties of orthogonal and selfadjoint operators and *to find the Jordan canonical form.
Syllabus
  • Affine geometry: affine spaces and subspaces, affine geometry and affine mappings. Linear forms: dual space, dual basis, dual homomorphism. Bilinear and quadratic forms: definition, matrix with respect to given basis, diagonalization, signature. Euklidean geometry: orthogonal projection, distance and deviation of affine subspaces. Linear operators: invariant subspaces, eigenvalues and eigen vectors, charakteristic polynomial, algebraic and geometric multiplicity of eigenvalues, conditions for diagonalization. Linear models. Ortogonal and unitar operators: definition and basic properties, eigenvalues, geometric meaning. Self adjoint operators: adjoint operator, symmetric and hermitian matrices, spectral decomposition. Jordan canonical form: nilpotent endomorphisms, root subspaces, computations.
Literature
  • Zlatoš P.: Lineárna algebra a geometria, připravovaná skripta MFF Univerzity Komenského v Bratislavě, elektronicky dostupné na http://www.math.muni.cz/pub/math/people/Paseka/lectures/LA/
  • Slovák, Jan. Lineární algebra. Učební texty. Brno:~Masarykova univerzita, 1998. 138. elektronicky dostupné na http://www.math.muni.cz/~slovak.
Teaching methods
Lectures and exercises (tutorials).
Assessment methods
Exam: written and oral. Requirements for the exam: to obtain 50% of points from 6 tests written during semester. Requirements: to manage the theory from the lecture, to be able to solve the problems similar to those from exercises
Language of instruction
Czech
Follow-Up Courses
Further comments (probably available only in Czech)
Study Materials
Information on completion of the course: ukončení zápočtem možné pouze rozhodnutím učitele
The course is taught annually.
Credit evaluation note: 2 kr. zápočet.
Listed among pre-requisites of other courses
Teacher's information
http://www.math.muni.cz/~cadek
The course is also listed under the following terms Spring 2008 - for the purpose of the accreditation, Spring 2011 - only for the accreditation, Spring 2000, Spring 2001, Spring 2002, Spring 2003, Spring 2004, Spring 2005, Spring 2006, Spring 2007, Spring 2008, Spring 2009, Spring 2010, Spring 2011, Spring 2012, spring 2012 - acreditation, Spring 2013, Spring 2014, Spring 2015, Spring 2016, Spring 2017, spring 2018, Spring 2019, Spring 2020, Spring 2021, Spring 2022, Spring 2024, Spring 2025.

M2110 Linear Algebra and Geometry II

Faculty of Science
Spring 2022
Extent and Intensity
2/2/0. 4 credit(s) (příf plus uk k 1 zk 2 plus 1 > 4). Recommended Type of Completion: zk (examination). Other types of completion: z (credit).
Teacher(s)
prof. RNDr. Jan Paseka, CSc. (lecturer)
doc. RNDr. Martin Čadek, CSc. (seminar tutor)
doc. Ilja Kossovskij, Ph.D. (seminar tutor)
Mgr. Mária Šimková (seminar tutor)
Guaranteed by
doc. RNDr. Martin Čadek, CSc.
Department of Mathematics and Statistics – Departments – Faculty of Science
Supplier department: Department of Mathematics and Statistics – Departments – Faculty of Science
Timetable
Wed 10:00–11:50 A,01026
  • Timetable of Seminar Groups:
M2110/01: Mon 16:00–17:50 M1,01017, J. Paseka
M2110/02: Wed 12:00–13:50 M1,01017, M. Čadek, M. Šimková
M2110/03: Mon 12:00–13:50 M1,01017, I. Kossovskij
Prerequisites
M1110 Linear Algebra I || M1111 Linear Algebra I ||( FI:MB003 Linear Algebra and Geometry I )
Knowledege of basic notion of linear algebra is supposed.
Course Enrolment Limitations
The course is also offered to the students of the fields other than those the course is directly associated with.
fields of study / plans the course is directly associated with
there are 7 fields of study the course is directly associated with, display
Course objectives
The aim of this second course in linear algebra is to introduce other basic notions of linear algebra. Passing the course the students *will know affine spaces, bilinear and quadratic forms, eingenvalues and eigenvectors of linear operators, *they will be able to solve problems concerning the spaces with scalar product and properties of orthogonal and selfadjoint operators and *to find the Jordan canonical form.
Learning outcomes
Passing the course the students *will know affine spaces, bilinear and quadratic forms, eingenvalues and eigenvectors of linear operators, *they will be able to solve problems concerning the spaces with scalar product and properties of orthogonal and selfadjoint operators and *to find the Jordan canonical form.
Syllabus
  • Affine geometry: affine spaces and subspaces, affine geometry and affine mappings. Linear forms: dual space, dual basis, dual homomorphism. Bilinear and quadratic forms: definition, matrix with respect to given basis, diagonalization, signature. Euklidean geometry: orthogonal projection, distance and deviation of affine subspaces. Linear operators: invariant subspaces, eigenvalues and eigen vectors, charakteristic polynomial, algebraic and geometric multiplicity of eigenvalues, conditions for diagonalization. Ortogonal and unitar operators: definition and basic properties, eigenvalues, geometric meaning. Self adjoint operators: adjoint operator, symmetric and hermitian matrices, spectral decomposition. Jordan canonical form: nilpotent endomorphisms, root subspaces, computations.
Literature
  • Zlatoš P.: Lineárna algebra a geometria, připravovaná skripta MFF Univerzity Komenského v Bratislavě, elektronicky dostupné na http://www.math.muni.cz/pub/math/people/Paseka/lectures/LA/
  • Slovák, Jan. Lineární algebra. Učební texty. Brno:~Masarykova univerzita, 1998. 138. elektronicky dostupné na http://www.math.muni.cz/~slovak.
Teaching methods
Lectures and exercises (tutorials).
Assessment methods
Exam: written and oral. Requirements for the exam: to obtain 50% of points from tests written during semester. Requirements: to manage the theory from the lecture, to be able to solve the problems similar to those from exercises
Language of instruction
Czech
Follow-Up Courses
Further comments (probably available only in Czech)
Study Materials
Information on completion of the course: ukončení zápočtem možné pouze rozhodnutím učitele
The course is taught annually.
Credit evaluation note: 2 kr. zápočet.
Listed among pre-requisites of other courses
Teacher's information
http://www.math.muni.cz/~cadek
The course is also listed under the following terms Spring 2008 - for the purpose of the accreditation, Spring 2011 - only for the accreditation, Spring 2000, Spring 2001, Spring 2002, Spring 2003, Spring 2004, Spring 2005, Spring 2006, Spring 2007, Spring 2008, Spring 2009, Spring 2010, Spring 2011, Spring 2012, spring 2012 - acreditation, Spring 2013, Spring 2014, Spring 2015, Spring 2016, Spring 2017, spring 2018, Spring 2019, Spring 2020, Spring 2021, Spring 2023, Spring 2024, Spring 2025.

M2110 Linear Algebra and Geometry II

Faculty of Science
Spring 2021
Extent and Intensity
2/2/0. 4 credit(s) (příf plus uk k 1 zk 2 plus 1 > 4). Recommended Type of Completion: zk (examination). Other types of completion: z (credit).
Teacher(s)
doc. RNDr. Martin Čadek, CSc. (lecturer)
doc. Ilja Kossovskij, Ph.D. (seminar tutor)
Mgr. Mária Šimková (seminar tutor)
prof. RNDr. Jan Paseka, CSc. (assistant)
Guaranteed by
doc. RNDr. Martin Čadek, CSc.
Department of Mathematics and Statistics – Departments – Faculty of Science
Supplier department: Department of Mathematics and Statistics – Departments – Faculty of Science
Timetable
Mon 1. 3. to Fri 14. 5. Tue 12:00–13:50 online_A
  • Timetable of Seminar Groups:
M2110/01: Mon 1. 3. to Fri 14. 5. Wed 12:00–13:50 online_M5, M. Čadek
M2110/02: Mon 1. 3. to Fri 14. 5. Wed 14:00–15:50 online_M1, M. Šimková
M2110/03: Mon 1. 3. to Fri 14. 5. Mon 14:00–15:50 online_M1, I. Kossovskij
Prerequisites
M1110 Linear Algebra I || M1111 Linear Algebra I ||( FI:MB003 Linear Algebra and Geometry I )
Knowledege of basic notion of linear algebra is supposed.
Course Enrolment Limitations
The course is also offered to the students of the fields other than those the course is directly associated with.
fields of study / plans the course is directly associated with
there are 7 fields of study the course is directly associated with, display
Course objectives
The aim of this second course in linear algebra is to introduce other basic notions of linear algebra. Passing the course the students *will know affine spaces, bilinear and quadratic forms, eingenvalues and eigenvectors of linear operators, *they will be able to solve problems concerning the spaces with scalar product and properties of orthogonal and selfadjoint operators and *to find the Jordan canonical form.
Learning outcomes
Passing the course the students *will know affine spaces, bilinear and quadratic forms, eingenvalues and eigenvectors of linear operators, *they will be able to solve problems concerning the spaces with scalar product and properties of orthogonal and selfadjoint operators and *to find the Jordan canonical form.
Syllabus
  • Affine geometry: affine spaces and subspaces, affine geometry and affine mappings. Linear forms: dual space, dual basis, dual homomorphism. Bilinear and quadratic forms: definition, matrix with respect to given basis, diagonalization, signature. Euklidean geometry: orthogonal projection, distance and deviation of affine subspaces. Linear operators: invariant subspaces, eigenvalues and eigen vectors, charakteristic polynomial, algebraic and geometric multiplicity of eigenvalues, conditions for diagonalization. Ortogonal and unitar operators: definition and basic properties, eigenvalues, geometric meaning. Self adjoint operators: adjoint operator, symmetric and hermitian matrices, spectral decomposition. Jordan canonical form: nilpotent endomorphisms, root subspaces, computations.
Literature
  • Zlatoš P.: Lineárna algebra a geometria, připravovaná skripta MFF Univerzity Komenského v Bratislavě, elektronicky dostupné na http://www.math.muni.cz/pub/math/people/Paseka/lectures/LA/
  • Slovák, Jan. Lineární algebra. Učební texty. Brno:~Masarykova univerzita, 1998. 138. elektronicky dostupné na http://www.math.muni.cz/~slovak.
Teaching methods
Lectures and exercises (tutorials) online.
Assessment methods
During semester you will get 10 homeworks. (10 points for any). There will be one written test during semester 10 points. Exam will conssists of written and oral part. To meet the demands from semester means to get at least 60 points. If you have more you will get bonification at most 4 points. To satisfy written part of the eaxam you have to get at least !& points for the sum bonification + test in semester+ computational part + theoretical part from 4+10+12+10=36 possible and simultaneously you have to get at least 5 points from the theoretical part of written exam.
Language of instruction
Czech
Follow-Up Courses
Further comments (probably available only in Czech)
Study Materials
Information on completion of the course: ukončení zápočtem možné pouze rozhodnutím učitele
The course is taught annually.
Credit evaluation note: 2 kr. zápočet.
Listed among pre-requisites of other courses
Teacher's information
http://www.math.muni.cz/~cadek
During semester you will get 10 homeworks. (10 points for any). There will be one written test during semester 10 points. Exam will conssists of written and oral part. To meet the demands from semester means to get at least 60 points. If you have more you will get bonification at most 4 points. To satisfy written part of the eaxam you have to get at least !& points for the sum bonification + test in semester+ computational part + theoretical part from 4+10+12+10=36 possible and simultaneously you have to get at least 5 points from the theoretical part of written exam.
The course is also listed under the following terms Spring 2008 - for the purpose of the accreditation, Spring 2011 - only for the accreditation, Spring 2000, Spring 2001, Spring 2002, Spring 2003, Spring 2004, Spring 2005, Spring 2006, Spring 2007, Spring 2008, Spring 2009, Spring 2010, Spring 2011, Spring 2012, spring 2012 - acreditation, Spring 2013, Spring 2014, Spring 2015, Spring 2016, Spring 2017, spring 2018, Spring 2019, Spring 2020, Spring 2022, Spring 2023, Spring 2024, Spring 2025.

M2110 Linear Algebra and Geometry II

Faculty of Science
Spring 2020
Extent and Intensity
2/2/0. 4 credit(s) (příf plus uk k 1 zk 2 plus 1 > 4). Recommended Type of Completion: zk (examination). Other types of completion: z (credit).
Teacher(s)
prof. RNDr. Jan Paseka, CSc. (lecturer)
doc. RNDr. Martin Čadek, CSc. (seminar tutor)
Mgr. David Kruml, Ph.D. (seminar tutor)
doc. Mgr. Lenka Zalabová, Ph.D. (assistant)
Guaranteed by
doc. RNDr. Martin Čadek, CSc.
Department of Mathematics and Statistics – Departments – Faculty of Science
Supplier department: Department of Mathematics and Statistics – Departments – Faculty of Science
Timetable
Wed 10:00–11:50 A,01026
  • Timetable of Seminar Groups:
M2110/01: Thu 10:00–11:50 M2,01021, J. Paseka
M2110/02: Wed 18:00–19:50 M1,01017, D. Kruml
M2110/03: Wed 14:00–15:50 M1,01017, M. Čadek
M2110/04: Tue 16:00–17:50 M1,01017, D. Kruml
Prerequisites
M1110 Linear Algebra I || M1111 Linear Algebra I ||( FI:MB003 Linear Algebra and Geometry I )
Knowledege of basic notion of linear algebra is supposed.
Course Enrolment Limitations
The course is also offered to the students of the fields other than those the course is directly associated with.
fields of study / plans the course is directly associated with
there are 7 fields of study the course is directly associated with, display
Course objectives
The aim of this second course in linear algebra is to introduce other basic notions of linear algebra. Passing the course the students *will know affine spaces, bilinear and quadratic forms, eingenvalues and eigenvectors of linear operators, *they will be able to solve problems concerning the spaces with scalar product and properties of orthogonal and selfadjoint operators and *to find the Jordan canonical form.
Learning outcomes
Passing the course the students *will know affine spaces, bilinear and quadratic forms, eingenvalues and eigenvectors of linear operators, *they will be able to solve problems concerning the spaces with scalar product and properties of orthogonal and selfadjoint operators and *to find the Jordan canonical form.
Syllabus
  • Affine geometry: affine spaces and subspaces, affine geometry and affine mappings. Linear forms: dual space, dual basis, dual homomorphism. Bilinear and quadratic forms: definition, matrix with respect to given basis, diagonalization, signature. Euklidean geometry: orthogonal projection, distance and deviation of affine subspaces. Linear operators: invariant subspaces, eigenvalues and eigen vectors, charakteristic polynomial, algebraic and geometric multiplicity of eigenvalues, conditions for diagonalization. Ortogonal and unitar operators: definition and basic properties, eigenvalues, geometric meaning. Self adjoint operators: adjoint operator, symmetric and hermitian matrices, spectral decomposition. Jordan canonical form: nilpotent endomorphisms, root subspaces, computations.
Literature
  • Zlatoš P.: Lineárna algebra a geometria, připravovaná skripta MFF Univerzity Komenského v Bratislavě, elektronicky dostupné na http://www.math.muni.cz/pub/math/people/Paseka/lectures/LA/
  • Slovák, Jan. Lineární algebra. Učební texty. Brno:~Masarykova univerzita, 1998. 138. elektronicky dostupné na http://www.math.muni.cz/~slovak.
Teaching methods
Lectures and exercises (tutorials).
Assessment methods
Exam: written and oral. Requirements for the exam: to obtain 50% of points from tests written during semester. Requirements: to manage the theory from the lecture, to be able to solve the problems similar to those from exercises
Language of instruction
Czech
Follow-Up Courses
Further comments (probably available only in Czech)
Study Materials
Information on completion of the course: ukončení zápočtem možné pouze rozhodnutím učitele
The course is taught annually.
Credit evaluation note: 2 kr. zápočet.
Listed among pre-requisites of other courses
Teacher's information
http://www.math.muni.cz/~cadek
The course is also listed under the following terms Spring 2008 - for the purpose of the accreditation, Spring 2011 - only for the accreditation, Spring 2000, Spring 2001, Spring 2002, Spring 2003, Spring 2004, Spring 2005, Spring 2006, Spring 2007, Spring 2008, Spring 2009, Spring 2010, Spring 2011, Spring 2012, spring 2012 - acreditation, Spring 2013, Spring 2014, Spring 2015, Spring 2016, Spring 2017, spring 2018, Spring 2019, Spring 2021, Spring 2022, Spring 2023, Spring 2024, Spring 2025.

M2110 Linear Algebra and Geometry II

Faculty of Science
Spring 2019
Extent and Intensity
2/2/0. 4 credit(s) (příf plus uk k 1 zk 2 plus 1 > 4). Recommended Type of Completion: zk (examination). Other types of completion: z (credit).
Teacher(s)
doc. RNDr. Martin Čadek, CSc. (lecturer)
doc. Ilja Kossovskij, Ph.D. (lecturer)
doc. RNDr. Jiří Kaďourek, CSc. (seminar tutor)
prof. RNDr. Jan Paseka, CSc. (seminar tutor)
Mgr. Tomáš Svoboda (seminar tutor)
Guaranteed by
doc. RNDr. Martin Čadek, CSc.
Department of Mathematics and Statistics – Departments – Faculty of Science
Supplier department: Department of Mathematics and Statistics – Departments – Faculty of Science
Timetable
Mon 18. 2. to Fri 17. 5. Tue 16:00–17:50 A,01026
  • Timetable of Seminar Groups:
M2110/01: Mon 18. 2. to Fri 17. 5. Tue 10:00–11:50 M4,01024, T. Svoboda
M2110/02: Mon 18. 2. to Fri 17. 5. Fri 14:00–15:50 M2,01021, J. Paseka
M2110/03: Mon 18. 2. to Fri 17. 5. Tue 14:00–15:50 M2,01021, J. Kaďourek
M2110/04: Mon 18. 2. to Fri 17. 5. Wed 12:00–13:50 M2,01021, J. Kaďourek
Prerequisites
M1110 Linear Algebra I || M1111 Linear Algebra I ||( FI:MB003 Linear Algebra and Geometry I )
Knowledege of basic notion of linear algebra is supposed.
Course Enrolment Limitations
The course is also offered to the students of the fields other than those the course is directly associated with.
fields of study / plans the course is directly associated with
Course objectives
The aim of this second course in linear algebra is to introduce other basic notions of linear algebra. Passing the course the students *will know affine spaces, bilinear and quadratic forms, eingenvalues and eigenvectors of linear operators, *they will be able to solve problems concerning the spaces with scalar product and properties of orthogonal and selfadjoint operators and *to find the Jordan canonical form.
Learning outcomes
Passing the course the students *will know affine spaces, bilinear and quadratic forms, eingenvalues and eigenvectors of linear operators, *they will be able to solve problems concerning the spaces with scalar product and properties of orthogonal and selfadjoint operators and *to find the Jordan canonical form.
Syllabus
  • Affine geometry: affine spaces and subspaces, affine geometry and affine mappings. Linear forms: dual space, dual basis, dual homomorphism. Bilinear and quadratic forms: definition, matrix with respect to given basis, diagonalization, signature. Euklidean geometry: orthogonal projection, distance and deviation of affine subspaces. Linear operators: invariant subspaces, eigenvalues and eigen vectors, charakteristic polynomial, algebraic and geometric multiplicity of eigenvalues, conditions for diagonalization. Ortogonal and unitar operators: definition and basic properties, eigenvalues, geometric meaning. Self adjoint operators: adjoint operator, symmetric and hermitian matrices, spectral decomposition. Jordan canonical form: nilpotent endomorphisms, root subspaces, computations.
Literature
  • Zlatoš P.: Lineárna algebra a geometria, připravovaná skripta MFF Univerzity Komenského v Bratislavě, elektronicky dostupné na http://www.math.muni.cz/pub/math/people/Paseka/lectures/LA/
  • Slovák, Jan. Lineární algebra. Učební texty. Brno:~Masarykova univerzita, 1998. 138. elektronicky dostupné na http://www.math.muni.cz/~slovak.
Teaching methods
Lectures and exercises (tutorials).
Assessment methods
Exam: written and oral. Requirements for the exam: to obtain 50% of points from tests written during semester. Requirements: to manage the theory from the lecture, to be able to solve the problems similar to those from exercises
Language of instruction
Czech
Follow-Up Courses
Further comments (probably available only in Czech)
Study Materials
Information on completion of the course: ukončení zápočtem možné pouze rozhodnutím učitele
The course is taught annually.
Credit evaluation note: 2 kr. zápočet.
Listed among pre-requisites of other courses
Teacher's information
http://www.math.muni.cz/~cadek
The course is also listed under the following terms Spring 2008 - for the purpose of the accreditation, Spring 2011 - only for the accreditation, Spring 2000, Spring 2001, Spring 2002, Spring 2003, Spring 2004, Spring 2005, Spring 2006, Spring 2007, Spring 2008, Spring 2009, Spring 2010, Spring 2011, Spring 2012, spring 2012 - acreditation, Spring 2013, Spring 2014, Spring 2015, Spring 2016, Spring 2017, spring 2018, Spring 2020, Spring 2021, Spring 2022, Spring 2023, Spring 2024, Spring 2025.

M2110 Linear Algebra and Geometry II

Faculty of Science
spring 2018
Extent and Intensity
2/2/0. 4 credit(s) (příf plus uk k 1 zk 2 plus 1 > 4). Recommended Type of Completion: zk (examination). Other types of completion: z (credit).
Teacher(s)
doc. RNDr. Martin Čadek, CSc. (lecturer)
doc. Lukáš Vokřínek, PhD. (lecturer)
doc. RNDr. Jiří Kaďourek, CSc. (seminar tutor)
prof. RNDr. Jan Paseka, CSc. (seminar tutor)
Guaranteed by
doc. RNDr. Martin Čadek, CSc.
Department of Mathematics and Statistics – Departments – Faculty of Science
Supplier department: Department of Mathematics and Statistics – Departments – Faculty of Science
Timetable
Thu 8:00–9:50 A,01026
  • Timetable of Seminar Groups:
M2110/01: Fri 12:00–13:50 M5,01013, J. Paseka
M2110/02: Fri 14:00–15:50 M5,01013, J. Paseka
M2110/03: Wed 8:00–9:50 M4,01024, J. Kaďourek
M2110/04: Tue 10:00–11:50 M1,01017, J. Kaďourek
Prerequisites
M1110 Linear Algebra I || M1111 Linear Algebra I ||( FI:MB003 Linear Algebra and Geometry I )
Knowledege of basic notion of linear algebra is supposed.
Course Enrolment Limitations
The course is also offered to the students of the fields other than those the course is directly associated with.
fields of study / plans the course is directly associated with
Course objectives
The aim of this second course in linear algebra is to introduce other basic notions of linear algebra. Passing the course the students *will know affine spaces, bilinear and quadratic forms, eingenvalues and eigenvectors of linear operators, *they will be able to solve problems concerning the spaces with scalar product and properties of orthogonal and selfadjoint operators and *to find the Jordan canonical form.
Learning outcomes
Passing the course the students *will know affine spaces, bilinear and quadratic forms, eingenvalues and eigenvectors of linear operators, *they will be able to solve problems concerning the spaces with scalar product and properties of orthogonal and selfadjoint operators and *to find the Jordan canonical form.
Syllabus
  • Affine geometry: affine spaces and subspaces, affine geometry and affine mappings. Linear forms: dual space, dual basis, dual homomorphism. Bilinear and quadratic forms: definition, matrix with respect to given basis, diagonalization, signature. Euklidean geometry: orthogonal projection, distance and deviation of affine subspaces. Linear operators: invariant subspaces, eigenvalues and eigen vectors, charakteristic polynomial, algebraic and geometric multiplicity of eigenvalues, conditions for diagonalization. Ortogonal and unitar operators: definition and basic properties, eigenvalues, geometric meaning. Self adjoint operators: adjoint operator, symmetric and hermitian matrices, spectral decomposition. Jordan canonical form: nilpotent endomorphisms, root subspaces, computations.
Literature
  • Zlatoš P.: Lineárna algebra a geometria, připravovaná skripta MFF Univerzity Komenského v Bratislavě, elektronicky dostupné na http://www.math.muni.cz/pub/math/people/Paseka/lectures/LA/
  • Slovák, Jan. Lineární algebra. Učební texty. Brno:~Masarykova univerzita, 1998. 138. elektronicky dostupné na http://www.math.muni.cz/~slovak.
Teaching methods
Lectures and exercises (tutorials).
Assessment methods
Exam: written and oral. Requirements for the exam: to obtain 50% of points from tests written during semester. Requirements: to manage the theory from the lecture, to be able to solve the problems similar to those from exercises
Language of instruction
Czech
Follow-Up Courses
Further comments (probably available only in Czech)
Study Materials
Information on completion of the course: ukončení zápočtem možné pouze rozhodnutím učitele
The course is taught annually.
Credit evaluation note: 2 kr. zápočet.
Listed among pre-requisites of other courses
Teacher's information
http://www.math.muni.cz/~cadek
The course is also listed under the following terms Spring 2008 - for the purpose of the accreditation, Spring 2011 - only for the accreditation, Spring 2000, Spring 2001, Spring 2002, Spring 2003, Spring 2004, Spring 2005, Spring 2006, Spring 2007, Spring 2008, Spring 2009, Spring 2010, Spring 2011, Spring 2012, spring 2012 - acreditation, Spring 2013, Spring 2014, Spring 2015, Spring 2016, Spring 2017, Spring 2019, Spring 2020, Spring 2021, Spring 2022, Spring 2023, Spring 2024, Spring 2025.

M2110 Linear Algebra and Geometry II

Faculty of Science
Spring 2017
Extent and Intensity
2/2/0. 4 credit(s) (příf plus uk k 1 zk 2 plus 1 > 4). Recommended Type of Completion: zk (examination). Other types of completion: z (credit).
Teacher(s)
doc. RNDr. Martin Čadek, CSc. (lecturer)
doc. RNDr. Jiří Kaďourek, CSc. (seminar tutor)
prof. RNDr. Jan Paseka, CSc. (seminar tutor)
Guaranteed by
doc. RNDr. Martin Čadek, CSc.
Department of Mathematics and Statistics – Departments – Faculty of Science
Supplier department: Department of Mathematics and Statistics – Departments – Faculty of Science
Timetable
Mon 20. 2. to Mon 22. 5. Wed 12:00–13:50 A,01026
  • Timetable of Seminar Groups:
M2110/01: Mon 20. 2. to Mon 22. 5. Wed 10:00–11:50 M2,01021, J. Kaďourek
M2110/02: Mon 20. 2. to Mon 22. 5. Wed 14:00–15:50 M2,01021, J. Kaďourek
M2110/03: Mon 20. 2. to Mon 22. 5. Fri 12:00–13:50 M2,01021, J. Paseka
M2110/04: Mon 20. 2. to Mon 22. 5. Fri 10:00–11:50 M2,01021, J. Paseka
Prerequisites
M1110 Linear Algebra I || M1111 Linear Algebra I ||( FI:MB003 Linear Algebra and Geometry I )
Knowledege of basic notion of linear algebra is supposed.
Course Enrolment Limitations
The course is also offered to the students of the fields other than those the course is directly associated with.
fields of study / plans the course is directly associated with
Course objectives
The aim of this second course in linear algebra is to introduce other basic notions of linear algebra. Passing the course the students *will know affine spaces, bilinear and quadratic forms, eingenvalues and eigenvectors of linear operators, *they will be able to solve problems concerning the spaces with scalar product and properties of orthogonal and selfadjoint operators and *to find the Jordan canonical form.
Learning outcomes
Passing the course the students *will know affine spaces, bilinear and quadratic forms, eingenvalues and eigenvectors of linear operators, *they will be able to solve problems concerning the spaces with scalar product and properties of orthogonal and selfadjoint operators and *to find the Jordan canonical form.
Syllabus
  • Affine geometry: affine spaces and subspaces, affine geometry and affine mappings. Linear forms: dual space, dual basis, dual homomorphism. Bilinear and quadratic forms: definition, matrix with respect to given basis, diagonalization, signature. Euklidean geometry: orthogonal projection, distance and deviation of affine subspaces. Linear operators: invariant subspaces, eigenvalues and eigen vectors, charakteristic polynomial, algebraic and geometric multiplicity of eigenvalues, conditions for diagonalization. Ortogonal and unitar operators: definition and basic properties, eigenvalues, geometric meaning. Self adjoint operators: adjoint operator, symmetric and hermitian matrices, spectral decomposition. Jordan canonical form: nilpotent endomorphisms, root subspaces, computations.
Literature
  • Zlatoš P.: Lineárna algebra a geometria, připravovaná skripta MFF Univerzity Komenského v Bratislavě, elektronicky dostupné na http://www.math.muni.cz/pub/math/people/Paseka/lectures/LA/
  • Slovák, Jan. Lineární algebra. Učební texty. Brno:~Masarykova univerzita, 1998. 138. elektronicky dostupné na http://www.math.muni.cz/~slovak.
Teaching methods
Lectures and exercises (tutorials).
Assessment methods
Exam: written and oral. Requirements for the exam: to obtain 50% of points from tests written during semester. Requirements: to manage the theory from the lecture, to be able to solve the problems similar to those from exercises
Language of instruction
Czech
Follow-Up Courses
Further comments (probably available only in Czech)
Study Materials
Information on completion of the course: ukončení zápočtem možné pouze rozhodnutím učitele
The course is taught annually.
Credit evaluation note: 2 kr. zápočet.
Listed among pre-requisites of other courses
Teacher's information
http://www.math.muni.cz/~cadek
The course is also listed under the following terms Spring 2008 - for the purpose of the accreditation, Spring 2011 - only for the accreditation, Spring 2000, Spring 2001, Spring 2002, Spring 2003, Spring 2004, Spring 2005, Spring 2006, Spring 2007, Spring 2008, Spring 2009, Spring 2010, Spring 2011, Spring 2012, spring 2012 - acreditation, Spring 2013, Spring 2014, Spring 2015, Spring 2016, spring 2018, Spring 2019, Spring 2020, Spring 2021, Spring 2022, Spring 2023, Spring 2024, Spring 2025.

M2110 Linear Algebra and Geometry II

Faculty of Science
Spring 2016
Extent and Intensity
2/2/0. 4 credit(s) (příf plus uk k 1 zk 2 plus 1 > 4). Recommended Type of Completion: zk (examination). Other types of completion: z (credit).
Teacher(s)
doc. RNDr. Martin Čadek, CSc. (lecturer)
doc. RNDr. Jiří Kaďourek, CSc. (seminar tutor)
Guaranteed by
doc. RNDr. Martin Čadek, CSc.
Department of Mathematics and Statistics – Departments – Faculty of Science
Supplier department: Department of Mathematics and Statistics – Departments – Faculty of Science
Timetable
Thu 8:00–9:50 A,01026
  • Timetable of Seminar Groups:
M2110/01: Thu 15:00–16:50 M4,01024, M. Čadek
M2110/02: Thu 12:00–13:50 M4,01024, M. Čadek
M2110/04: Wed 14:00–15:50 M2,01021, J. Kaďourek
Prerequisites
M1110 Linear Algebra I || M1111 Linear Algebra I ||( FI:MB003 Linear Algebra and Geometry I )
Knowledege of basic notion of linear algebra is supposed.
Course Enrolment Limitations
The course is also offered to the students of the fields other than those the course is directly associated with.
fields of study / plans the course is directly associated with
Course objectives
The aim of this second course in linear algebra is to introduce other basic notions of linear algebra. Passing the course the students *will know affine spaces, bilinear and quadratic forms, eingenvalues and eigenvectors of linear operators, *they will be able to solve problems concerning the spaces with scalar product and properties of orthogonal and selfadjoint operators and *to find the Jordan canonical form.
Syllabus
  • Affine geometry: affine spaces and subspaces, affine geometry and affine mappings. Linear forms: dual space, dual basis, dual homomorphism. Bilinear and quadratic forms: definition, matrix with respect to given basis, diagonalization, signature. Euklidean geometry: orthogonal projection, distance and deviation of affine subspaces. Linear operators: invariant subspaces, eigenvalues and eigen vectors, charakteristic polynomial, algebraic and geometric multiplicity of eigenvalues, conditions for diagonalization. Ortogonal and unitar operators: definition and basic properties, eigenvalues, geometric meaning. Self adjoint operators: adjoint operator, symmetric and hermitian matrices, spectral decomposition. Jordan canonical form: nilpotent endomorphisms, root subspaces, computations.
Literature
  • Zlatoš P.: Lineárna algebra a geometria, připravovaná skripta MFF Univerzity Komenského v Bratislavě, elektronicky dostupné na http://www.math.muni.cz/pub/math/people/Paseka/lectures/LA/
  • Slovák, Jan. Lineární algebra. Učební texty. Brno:~Masarykova univerzita, 1998. 138. elektronicky dostupné na http://www.math.muni.cz/~slovak.
Teaching methods
Lectures and exercises (tutorials).
Assessment methods
Exam: written and oral. Requirements for the exam: to obtain 50% of points from tests written during semester. Requirements: to manage the theory from the lecture, to be able to solve the problems similar to those from exercises
Language of instruction
Czech
Follow-Up Courses
Further comments (probably available only in Czech)
Study Materials
Information on completion of the course: ukončení zápočtem možné pouze rozhodnutím učitele
The course is taught annually.
Credit evaluation note: 2 kr. zápočet.
Listed among pre-requisites of other courses
Teacher's information
http://www.math.muni.cz/~cadek
The course is also listed under the following terms Spring 2008 - for the purpose of the accreditation, Spring 2011 - only for the accreditation, Spring 2000, Spring 2001, Spring 2002, Spring 2003, Spring 2004, Spring 2005, Spring 2006, Spring 2007, Spring 2008, Spring 2009, Spring 2010, Spring 2011, Spring 2012, spring 2012 - acreditation, Spring 2013, Spring 2014, Spring 2015, Spring 2017, spring 2018, Spring 2019, Spring 2020, Spring 2021, Spring 2022, Spring 2023, Spring 2024, Spring 2025.

M2110 Linear Algebra and Geometry II

Faculty of Science
Spring 2015
Extent and Intensity
2/2/0. 4 credit(s) (příf plus uk k 1 zk 2 plus 1 > 4). Recommended Type of Completion: zk (examination). Other types of completion: z (credit).
Teacher(s)
doc. RNDr. Martin Čadek, CSc. (lecturer)
doc. RNDr. Jiří Kaďourek, CSc. (seminar tutor)
prof. RNDr. Jan Paseka, CSc. (seminar tutor)
Guaranteed by
doc. RNDr. Martin Čadek, CSc.
Department of Mathematics and Statistics – Departments – Faculty of Science
Supplier department: Department of Mathematics and Statistics – Departments – Faculty of Science
Timetable
Thu 8:00–9:50 A,01026
  • Timetable of Seminar Groups:
M2110/01: Tue 12:00–13:50 M5,01013, M. Čadek
M2110/02: Tue 16:00–17:50 M5,01013, J. Kaďourek
M2110/03: Thu 10:00–11:50 M2,01021, J. Kaďourek
M2110/04: Fri 9:00–10:50 M4,01024, J. Paseka
M2110/05: Fri 12:00–13:50 M4,01024, J. Paseka
Prerequisites
M1110 Linear Algebra I || M1111 Linear Algebra I ||( FI:MB003 Linear Algebra and Geometry I )
Knowledege of basic notion of linear algebra is supposed.
Course Enrolment Limitations
The course is also offered to the students of the fields other than those the course is directly associated with.
fields of study / plans the course is directly associated with
there are 6 fields of study the course is directly associated with, display
Course objectives
The aim of this second course in linear algebra is to introduce other basic notions of linear algebra. Passing the course the students *will know affine spaces, bilinear and quadratic forms, eingenvalues and eigenvectors of linear operators, *they will be able to solve problems concerning the spaces with scalar product and properties of orthogonal and selfadjoint operators and *to find the Jordan canonical form.
Syllabus
  • Affine geometry: affine spaces and subspaces, affine geometry and affine mappings. Linear forms: dual space, dual basis, dual homomorphism. Bilinear and quadratic forms: definition, matrix with respect to given basis, diagonalization, signature. Euklidean geometry: orthogonal projection, distance and deviation of affine subspaces. Linear operators: invariant subspaces, eigenvalues and eigen vectors, charakteristic polynomial, algebraic and geometric multiplicity of eigenvalues, conditions for diagonalization. Ortogonal and unitar operators: definition and basic properties, eigenvalues, geometric meaning. Self adjoint operators: adjoint operator, symmetric and hermitian matrices, spectral decomposition. Jordan canonical form: nilpotent endomorphisms, root subspaces, computations.
Literature
  • Zlatoš P.: Lineárna algebra a geometria, připravovaná skripta MFF Univerzity Komenského v Bratislavě, elektronicky dostupné na http://www.math.muni.cz/pub/math/people/Paseka/lectures/LA/
  • Slovák, Jan. Lineární algebra. Učební texty. Brno:~Masarykova univerzita, 1998. 138. elektronicky dostupné na http://www.math.muni.cz/~slovak.
Teaching methods
Lectures and exercises (tutorials).
Assessment methods
Exam: written and oral. Requirements for the exam: to obtain 50% of points from tests written during semester. Requirements: to manage the theory from the lecture, to be able to solve the problems similar to those from exercises
Language of instruction
Czech
Follow-Up Courses
Further comments (probably available only in Czech)
Study Materials
Information on completion of the course: ukončení zápočtem možné pouze rozhodnutím učitele
The course is taught annually.
Credit evaluation note: 2 kr. zápočet.
Listed among pre-requisites of other courses
Teacher's information
http://www.math.muni.cz/~cadek
The course is also listed under the following terms Spring 2008 - for the purpose of the accreditation, Spring 2011 - only for the accreditation, Spring 2000, Spring 2001, Spring 2002, Spring 2003, Spring 2004, Spring 2005, Spring 2006, Spring 2007, Spring 2008, Spring 2009, Spring 2010, Spring 2011, Spring 2012, spring 2012 - acreditation, Spring 2013, Spring 2014, Spring 2016, Spring 2017, spring 2018, Spring 2019, Spring 2020, Spring 2021, Spring 2022, Spring 2023, Spring 2024, Spring 2025.

M2110 Linear Algebra and Geometry II

Faculty of Science
Spring 2014
Extent and Intensity
2/2/0. 4 credit(s) (příf plus uk k 1 zk 2 plus 1 > 4). Recommended Type of Completion: zk (examination). Other types of completion: z (credit).
Teacher(s)
doc. RNDr. Martin Čadek, CSc. (lecturer)
doc. Lukáš Vokřínek, PhD. (lecturer)
Mgr. Marek Filakovský, Ph.D. (seminar tutor)
doc. RNDr. Jiří Kaďourek, CSc. (seminar tutor)
prof. RNDr. Jan Paseka, CSc. (seminar tutor)
Guaranteed by
doc. RNDr. Martin Čadek, CSc.
Department of Mathematics and Statistics – Departments – Faculty of Science
Supplier department: Department of Mathematics and Statistics – Departments – Faculty of Science
Timetable
Mon 12:00–13:50 A,01026
  • Timetable of Seminar Groups:
M2110/01: Mon 14:00–15:50 M2,01021, M. Čadek
M2110/02: Wed 12:00–13:50 M5,01013, J. Kaďourek
M2110/03: Tue 10:00–11:50 M2,01021, J. Kaďourek
M2110/04: Fri 14:00–15:50 M2,01021, J. Paseka
M2110/05: Fri 12:00–13:50 M2,01021, J. Paseka
Prerequisites
M1110 Linear Algebra I || M1111 Linear Algebra I ||( FI:MB003 Linear Algebra and Geometry I )
Knowledege of basic notion of linear algebra is supposed.
Course Enrolment Limitations
The course is also offered to the students of the fields other than those the course is directly associated with.
fields of study / plans the course is directly associated with
there are 6 fields of study the course is directly associated with, display
Course objectives
The aim of this second course in linear algebra is to introduce other basic notions of linear algebra. Passing the course the students *will know affine spaces, bilinear and quadratic forms, eingenvalues and eigenvectors of linear operators, *they will be able to solve problems concerning the spaces with scalar product and properties of orthogonal and selfadjoint operators and *to find the Jordan canonical form.
Syllabus
  • Affine geometry: affine spaces and subspaces, affine geometry and affine mappings. Linear forms: dual space, dual basis, dual homomorphism. Bilinear and quadratic forms: definition, matrix with respect to given basis, diagonalization, signature. Euklidean geometry: orthogonal projection, distance and deviation of affine subspaces. Linear operators: invariant subspaces, eigenvalues and eigen vectors, charakteristic polynomial, algebraic and geometric multiplicity of eigenvalues, conditions for diagonalization. Ortogonal and unitar operators: definition and basic properties, eigenvalues, geometric meaning. Self adjoint operators: adjoint operator, symmetric and hermitian matrices, spectral decomposition. Jordan canonical form: nilpotent endomorphisms, root subspaces, computations.
Literature
  • Zlatoš P.: Lineárna algebra a geometria, připravovaná skripta MFF Univerzity Komenského v Bratislavě, elektronicky dostupné na http://www.math.muni.cz/pub/math/people/Paseka/lectures/LA/
  • Slovák, Jan. Lineární algebra. Učební texty. Brno:~Masarykova univerzita, 1998. 138. elektronicky dostupné na http://www.math.muni.cz/~slovak.
Teaching methods
Lectures and exercises (tutorials).
Assessment methods
Exam: written and oral. Requirements for the exam: to obtain 50% of points from tests written during semester. Requirements: to manage the theory from the lecture, to be able to solve the problems similar to those from exercises
Language of instruction
Czech
Follow-Up Courses
Further comments (probably available only in Czech)
Study Materials
Information on completion of the course: ukončení zápočtem možné pouze rozhodnutím učitele
The course is taught annually.
Credit evaluation note: 2 kr. zápočet.
Listed among pre-requisites of other courses
Teacher's information
http://www.math.muni.cz/~cadek
The course is also listed under the following terms Spring 2008 - for the purpose of the accreditation, Spring 2011 - only for the accreditation, Spring 2000, Spring 2001, Spring 2002, Spring 2003, Spring 2004, Spring 2005, Spring 2006, Spring 2007, Spring 2008, Spring 2009, Spring 2010, Spring 2011, Spring 2012, spring 2012 - acreditation, Spring 2013, Spring 2015, Spring 2016, Spring 2017, spring 2018, Spring 2019, Spring 2020, Spring 2021, Spring 2022, Spring 2023, Spring 2024, Spring 2025.

M2110 Linear Algebra and Geometry II

Faculty of Science
Spring 2013
Extent and Intensity
2/2/0. 4 credit(s) (příf plus uk k 1 zk 2 plus 1 > 4). Recommended Type of Completion: zk (examination). Other types of completion: z (credit).
Teacher(s)
doc. RNDr. Martin Čadek, CSc. (lecturer)
doc. RNDr. Jiří Kaďourek, CSc. (seminar tutor)
prof. RNDr. Jan Paseka, CSc. (seminar tutor)
doc. Lukáš Vokřínek, PhD. (seminar tutor)
Guaranteed by
doc. RNDr. Martin Čadek, CSc.
Department of Mathematics and Statistics – Departments – Faculty of Science
Supplier department: Department of Mathematics and Statistics – Departments – Faculty of Science
Timetable
Mon 12:00–13:50 A,01026
  • Timetable of Seminar Groups:
M2110/01: Tue 14:00–15:50 M2,01021, L. Vokřínek
M2110/02: Thu 12:00–13:50 M2,01021, J. Kaďourek
M2110/03: Thu 14:00–15:50 M2,01021, J. Kaďourek
M2110/04: Fri 10:00–11:50 M2,01021, J. Paseka
M2110/05: Fri 12:00–13:50 M2,01021, J. Paseka
Prerequisites
M1110 Linear Algebra I || M1111 Linear Algebra I ||( FI:MB003 Linear Algebra and Geometry I )
Knowledege of basic notion of linear algebra is supposed.
Course Enrolment Limitations
The course is also offered to the students of the fields other than those the course is directly associated with.
fields of study / plans the course is directly associated with
there are 15 fields of study the course is directly associated with, display
Course objectives
The aim of this second course in linear algebra is to introduce other basic notions of linear algebra. Passing the course the stuidents *will know affine spaces, bilinear and quadratic forms, eingenvalues and eigenvectors of linear operators, *they will be able to solve problems concerning the spaces with scalar product and properties of orthogonal and selfadjoint operators and *to find the Jordan canonical form.
Syllabus
  • Affine geometry: affine spaces and subspaces, affine geometry and affine mappings. Linear forms: dual space, dual basis, dual homomorphism. Bilinear and quadratic forms: definition, matrix with respect to given basis, diagonalization, signature. Euklidean geometry: orthogonal projection, distance and deviation of affine subspaces. Linear operators: invariant subspaces, eigenvalues and eigen vectors, charakteristic polynomial, algebraic and geometric multiplicity of eigenvalues, conditions for diagonalization. Ortogonal a unitar operators: definition and basic properties, eigenvalues, geometric meaning. Self adjoint operators: adjoint operator, symmetric and hermitian matrices, spectral decomposition. Jordan canonical form: nilpotent endomorphisms, root subspaces, computations.
Literature
  • Zlatoš P.: Lineárna algebra a geometria, připravovaná skripta MFF Univerzity Komenského v Bratislavě, elektronicky dostupné na http://www.math.muni.cz/pub/math/people/Paseka/lectures/LA/
  • Slovák, Jan. Lineární algebra. Učební texty. Brno:~Masarykova univerzita, 1998. 138. elektronicky dostupné na http://www.math.muni.cz/~slovak.
Teaching methods
Lectures and exercises (tutorials).
Assessment methods
Exam: witten and oral. Requirements to the exam: to obtain 50% of points from tests written during semester.
Language of instruction
Czech
Follow-Up Courses
Further comments (probably available only in Czech)
Study Materials
Information on completion of the course: ukončení zápočtem možné pouze rozhodnutím učitele
The course is taught annually.
Credit evaluation note: 2 kr. zápočet.
Listed among pre-requisites of other courses
Teacher's information
http://www.math.muni.cz/~cadek
The course is also listed under the following terms Spring 2008 - for the purpose of the accreditation, Spring 2011 - only for the accreditation, Spring 2000, Spring 2001, Spring 2002, Spring 2003, Spring 2004, Spring 2005, Spring 2006, Spring 2007, Spring 2008, Spring 2009, Spring 2010, Spring 2011, Spring 2012, spring 2012 - acreditation, Spring 2014, Spring 2015, Spring 2016, Spring 2017, spring 2018, Spring 2019, Spring 2020, Spring 2021, Spring 2022, Spring 2023, Spring 2024, Spring 2025.

M2110 Linear Algebra and Geometry II

Faculty of Science
Spring 2012
Extent and Intensity
2/2/0. 4 credit(s) (příf plus uk k 1 zk 2 plus 1 > 4). Recommended Type of Completion: zk (examination). Other types of completion: z (credit).
Teacher(s)
doc. RNDr. Martin Čadek, CSc. (lecturer)
Mgr. Jiří Janda, Ph.D. (seminar tutor)
doc. RNDr. Jiří Kaďourek, CSc. (seminar tutor)
doc. Mgr. Ondřej Klíma, Ph.D. (seminar tutor)
RNDr. Mgr. Miroslav Korbelář, Ph.D. (seminar tutor)
Guaranteed by
doc. RNDr. Martin Čadek, CSc.
Department of Mathematics and Statistics – Departments – Faculty of Science
Supplier department: Department of Mathematics and Statistics – Departments – Faculty of Science
Timetable
Thu 8:00–9:50 A,01026
  • Timetable of Seminar Groups:
M2110/02: Wed 12:00–13:50 M5,01013, J. Kaďourek, M. Korbelář
M2110/03: Wed 18:00–19:50 M2,01021, J. Janda
M2110/04: Fri 12:00–13:50 M1,01017, O. Klíma
M2110/05: Thu 10:00–11:50 M2,01021, M. Čadek
Prerequisites
M1110 Linear Algebra I || M1111 Linear Algebra I ||( FI:MB003 Linear Algebra and Geometry I )
Knowledege of basic notion of linear algebra is supposed.
Course Enrolment Limitations
The course is also offered to the students of the fields other than those the course is directly associated with.
fields of study / plans the course is directly associated with
there are 11 fields of study the course is directly associated with, display
Course objectives
The aim of this second course in linear algebra is to introduce other basic notions of linear algebra. Passing the course the stuidents *will know affine spaces, bilinear and quadratic forms, eingenvalues and eigenvectors of linear operators, *they will be able to solve problems concerning the spaces with scalar product and properties of orthogonal and selfadjoint operators and *to find the Jordan canonical form.
Syllabus
  • Affine geometry: affine spaces and subspaces, affine geometry and affine mappings. Linear forms: dual space, dual basis, dual homomorphism. Bilinear and quadratic forms: definition, matrix with respect to given basis, diagonalization, signature. Euklidean geometry: orthogonal projection, distance and deviation of affine subspaces. Linear operators: invariant subspaces, eigenvalues and eigen vectors, charakteristic polynomial, algebraic and geometric multiplicity of eigenvalues, conditions for diagonalization. Ortogonal a unitar operators: definition and basic properties, eigenvalues, geometric meaning. Self adjoint operators: adjoint operator, symmetric and hermitian matrices, spectral decomposition. Jordan canonical form: nilpotent endomorphisms, root subspaces, computations.
Literature
  • Zlatoš P.: Lineárna algebra a geometria, připravovaná skripta MFF Univerzity Komenského v Bratislavě, elektronicky dostupné na http://www.math.muni.cz/pub/math/people/Paseka/lectures/LA/
  • Slovák, Jan. Lineární algebra. Učební texty. Brno:~Masarykova univerzita, 1998. 138. elektronicky dostupné na http://www.math.muni.cz/~slovak.
Teaching methods
Lectures and exercises (tutorials).
Assessment methods
Exam has three parts: short tests during semester, witten and oral. Requirements to the written exam: to obtain sufficient amount of points during semester.
Language of instruction
Czech
Follow-Up Courses
Further comments (probably available only in Czech)
Study Materials
Information on completion of the course: ukončení zápočtem možné pouze rozhodnutím učitele
The course is taught annually.
Credit evaluation note: 2 kr. zápočet.
Listed among pre-requisites of other courses
Teacher's information
http://www.math.muni.cz/~cadek
The course is also listed under the following terms Spring 2008 - for the purpose of the accreditation, Spring 2011 - only for the accreditation, Spring 2000, Spring 2001, Spring 2002, Spring 2003, Spring 2004, Spring 2005, Spring 2006, Spring 2007, Spring 2008, Spring 2009, Spring 2010, Spring 2011, spring 2012 - acreditation, Spring 2013, Spring 2014, Spring 2015, Spring 2016, Spring 2017, spring 2018, Spring 2019, Spring 2020, Spring 2021, Spring 2022, Spring 2023, Spring 2024, Spring 2025.

M2110 Linear Algebra and Geometry II

Faculty of Science
Spring 2011
Extent and Intensity
2/2/0. 4 credit(s) (příf plus uk k 1 zk 2 plus 1 > 4). Recommended Type of Completion: zk (examination). Other types of completion: z (credit).
Teacher(s)
doc. RNDr. Martin Čadek, CSc. (lecturer)
doc. RNDr. Jiří Kaďourek, CSc. (seminar tutor)
doc. Mgr. Ondřej Klíma, Ph.D. (seminar tutor)
doc. Lukáš Vokřínek, PhD. (seminar tutor)
Guaranteed by
doc. RNDr. Martin Čadek, CSc.
Department of Mathematics and Statistics – Departments – Faculty of Science
Timetable
Tue 14:00–15:50 A,01026
  • Timetable of Seminar Groups:
M2110/01: Tue 10:00–11:50 M5,01013, O. Klíma
M2110/02: Wed 14:00–15:50 M1,01017, J. Kaďourek
M2110/03: Wed 16:00–17:50 M1,01017, J. Kaďourek
M2110/04: Wed 16:00–17:50 M5,01013, L. Vokřínek
M2110/05: Wed 14:00–15:50 M5,01013, L. Vokřínek
M2110/06: Mon 8:00–9:50 M2,01021, M. Čadek
Prerequisites
M1110 Linear Algebra I || M1111 Linear Algebra I ||( FI:MB003 Linear Algebra and Geometry I )
Knowledege of basic notion of linear algebra is supposed.
Course Enrolment Limitations
The course is also offered to the students of the fields other than those the course is directly associated with.
fields of study / plans the course is directly associated with
there are 12 fields of study the course is directly associated with, display
Course objectives
The aim of this second course in linear algebra is to introduce other basic notions of linear algebra. Passing the course the stuidents *will know affine spaces, bilinear and quadratic forms, eingenvalues and eigenvectors of linear operators, *they will be able to solve problems concerning the spaces with scalar product and properties of orthogonal and selfadjoint operators and *to find the Jordan canonical form.
Syllabus
  • Affine geometry: affine spaces and subspaces, affine geometry and affine mappings. Linear forms: dual space, dual basis, dual homomorphism. Bilinear and quadratic forms: definition, matrix with respect to given basis, diagonalization, signature. Euklidean geometry: orthogonal projection, distance and deviation of affine subspaces. Linear operators: invariant subspaces, eigenvalues and eigen vectors, charakteristic polynomial, algebraic and geometric multiplicity of eigenvalues, conditions for diagonalization. Ortogonal a unitar operators: definition and basic properties, eigenvalues, geometric meaning. Self adjoint operators: adjoint operator, symmetric and hermitian matrices, spectral decomposition. Jordan canonical form: nilpotent endomorphisms, root subspaces, computations.
Literature
  • Zlatoš P.: Lineárna algebra a geometria, připravovaná skripta MFF Univerzity Komenského v Bratislavě, elektronicky dostupné na http://www.math.muni.cz/pub/math/people/Paseka/lectures/LA/
  • Slovák, Jan. Lineární algebra. Učební texty. Brno:~Masarykova univerzita, 1998. 138. elektronicky dostupné na http://www.math.muni.cz/~slovak.
Teaching methods
Lectures and exercises (tutorials).
Assessment methods
Exam: witten and oral.
Language of instruction
Czech
Follow-Up Courses
Further comments (probably available only in Czech)
Study Materials
Information on completion of the course: ukončení zápočtem možné pouze rozhodnutím učitele
The course is taught annually.
Credit evaluation note: 2 kr. zápočet.
Listed among pre-requisites of other courses
Teacher's information
http://www.math.muni.cz/~cadek
The course is also listed under the following terms Spring 2008 - for the purpose of the accreditation, Spring 2011 - only for the accreditation, Spring 2000, Spring 2001, Spring 2002, Spring 2003, Spring 2004, Spring 2005, Spring 2006, Spring 2007, Spring 2008, Spring 2009, Spring 2010, Spring 2012, spring 2012 - acreditation, Spring 2013, Spring 2014, Spring 2015, Spring 2016, Spring 2017, spring 2018, Spring 2019, Spring 2020, Spring 2021, Spring 2022, Spring 2023, Spring 2024, Spring 2025.

M2110 Linear Algebra and Geometry II

Faculty of Science
Spring 2010
Extent and Intensity
2/2/0. 4 credit(s) (fasci plus compl plus > 4). Recommended Type of Completion: zk (examination). Other types of completion: z (credit).
Teacher(s)
doc. RNDr. Martin Čadek, CSc. (lecturer)
doc. Mgr. Josef Šilhan, Ph.D. (lecturer)
doc. RNDr. Jiří Kaďourek, CSc. (seminar tutor)
doc. Mgr. Ondřej Klíma, Ph.D. (seminar tutor)
Mgr. David Kruml, Ph.D. (seminar tutor)
Guaranteed by
doc. RNDr. Martin Čadek, CSc.
Department of Mathematics and Statistics – Departments – Faculty of Science
Timetable
Mon 12:00–13:50 A,01026
  • Timetable of Seminar Groups:
M2110/01: Wed 14:00–15:50 M5,01013, J. Šilhan
M2110/02: Thu 14:00–15:50 M2,01021, O. Klíma
M2110/03: Thu 16:00–17:50 M2,01021, O. Klíma
M2110/04: Thu 8:00–9:50 M1,01017, D. Kruml
M2110/05: No timetable has been entered into IS. J. Šilhan
M2110/06: Thu 11:00–12:50 M4,01024, D. Kruml
Prerequisites
M1110 Linear Algebra I || M1111 Linear Algebra I ||( FI:MB003 Linear Algebra and Geometry I )
Knowledege of basic notion of linear algebra is supposed.
Course Enrolment Limitations
The course is also offered to the students of the fields other than those the course is directly associated with.
fields of study / plans the course is directly associated with
there are 12 fields of study the course is directly associated with, display
Course objectives
The aim of this second course in linear algebra is to introduce other basic notions of linear algebra. Passing the course the stuidents *will know affine spaces, bilinear and quadratic forms, eingenvalues and eigenvectors of linear operators, *they will be able to solve problems concerning the spaces with scalar product and properties of orthogonal and selfadjoint operators and *to find the Jordan canonical form.
Syllabus
  • Affine geometry: affine spaces and subspaces, affine geometry and affine mappings. Linear forms: dual space, dual basis, dual homomorphism. Bilinear and quadratic forms: definition, matrix with respect to given basis, diagonalization, signature. Euklidean geometry: orthogonal projection, distance and deviation of affine subspaces. Linear operators: invariant subspaces, eigenvalues and eigen vectors, charakteristic polynomial, algebraic and geometric multiplicity of eigenvalues, conditions for diagonalization. Ortogonal a unitar operators: definition and basic properties, eigenvalues, geometric meaning. Self adjoint operators: adjoint operator, symmetric and hermitian matrices, spectral decomposition. Jordan canonical form: nilpotent endomorphisms, root subspaces, computations.
Literature
  • Zlatoš P.: Lineárna algebra a geometria, připravovaná skripta MFF Univerzity Komenského v Bratislavě, elektronicky dostupné na http://www.math.muni.cz/pub/math/people/Paseka/lectures/LA/
  • Slovák, Jan. Lineární algebra. Učební texty. Brno:~Masarykova univerzita, 1998. 138. elektronicky dostupné na http://www.math.muni.cz/~slovak.
Teaching methods
Lectures and exercises (tutorials).
Assessment methods
Exam: witten and oral. Requirements to the exam: to obtain internal credit from exercises.
Language of instruction
Czech
Follow-Up Courses
Further comments (probably available only in Czech)
Study Materials
Information on completion of the course: ukončení zápočtem možné pouze rozhodnutím učitele
The course is taught annually.
Credit evaluation note: 2 kr. zápočet.
Listed among pre-requisites of other courses
Teacher's information
http://www.math.muni.cz/~cadek
The course is also listed under the following terms Spring 2008 - for the purpose of the accreditation, Spring 2011 - only for the accreditation, Spring 2000, Spring 2001, Spring 2002, Spring 2003, Spring 2004, Spring 2005, Spring 2006, Spring 2007, Spring 2008, Spring 2009, Spring 2011, Spring 2012, spring 2012 - acreditation, Spring 2013, Spring 2014, Spring 2015, Spring 2016, Spring 2017, spring 2018, Spring 2019, Spring 2020, Spring 2021, Spring 2022, Spring 2023, Spring 2024, Spring 2025.

M2110 Linear Algebra and Geometry II

Faculty of Science
Spring 2009
Extent and Intensity
2/2/0. 4 credit(s) (fasci plus compl plus > 4). Recommended Type of Completion: zk (examination). Other types of completion: z (credit).
Teacher(s)
doc. RNDr. Martin Čadek, CSc. (lecturer)
Mgr. Oldřich Spáčil (seminar tutor)
Mgr. Radek Šlesinger, Ph.D. (seminar tutor)
Guaranteed by
doc. RNDr. Martin Čadek, CSc.
Department of Mathematics and Statistics – Departments – Faculty of Science
Timetable
Wed 11:00–12:50 A,01026
  • Timetable of Seminar Groups:
M2110/01: Mon 17:00–18:50 M1,01017, O. Spáčil
M2110/02: Tue 16:00–17:50 M1,01017, R. Šlesinger
M2110/03: Wed 18:00–19:50 M5,01013, O. Spáčil
M2110/04: Tue 18:00–19:50 M1,01017, R. Šlesinger
Prerequisites
M1110 Linear Algebra I || M1111 Linear Algebra I ||( FI:MB003 Linear Algebra and Geometry I )
Knowledege of basic notion of linear algebra is supposed.
Course Enrolment Limitations
The course is also offered to the students of the fields other than those the course is directly associated with.
fields of study / plans the course is directly associated with
there are 11 fields of study the course is directly associated with, display
Course objectives
The aim of this second course in linear algebra is to introduce other basic notions such as affine and projective spaces, bilinear and quadratic forms, eingenvalues and eigenvectors of linear operators. In more details the spaces with scalar product and properties of orthogonal and selfadjoint operators are examined. All is applied in affine and Euclidean geometry. At the end we deal with the Jordan canonical form.
Syllabus
  • Affine geometry: affine spaces and subspaces, affine geometry and affine mappings. Linear forms: dual space, dual basis, dual homomorphism. Bilinear and quadratic forms: definition, matrix with respect to given basis, diagonalization, signature. Euklidean geometry: orthogonal projection, distance and deviation of affine subspaces. Linear operators: invariant subspaces, eigenvalues and eigen vectors, charakteristic polynomial, algebraic and geometric multiplicity of eigenvalues, conditions for diagonalization. Ortogonal a unitar operators: definition and basic properties, eigenvalues, geometric meaning. Self adjoint operators: adjoint operator, symmetric and hermitian matrices, spectral decomposition. Jordan canonical form: nilpotent endomorphisms, root subspaces, computations.
Literature
  • Zlatoš P.: Lineárna algebra a geometria, připravovaná skripta MFF Univerzity Komenského v Bratislavě, elektronicky dostupné na http://www.math.muni.cz/pub/math/people/Paseka/lectures/LA/
  • Slovák, Jan. Lineární algebra. Učební texty. Brno:~Masarykova univerzita, 1998. 138. elektronicky dostupné na http://www.math.muni.cz/~slovak.
Assessment methods
Form: lectures and exercises. Exam: witten and oral. Requirements to the exam: to obtain internal credit from exercuises.
Language of instruction
Czech
Follow-Up Courses
Further comments (probably available only in Czech)
Information on completion of the course: ukončení zápočtem možné pouze rozhodnutím učitele
The course is taught annually.
Credit evaluation note: 2 kr. zápočet.
Listed among pre-requisites of other courses
Teacher's information
http://www.math.muni.cz/~cadek
The course is also listed under the following terms Spring 2008 - for the purpose of the accreditation, Spring 2011 - only for the accreditation, Spring 2000, Spring 2001, Spring 2002, Spring 2003, Spring 2004, Spring 2005, Spring 2006, Spring 2007, Spring 2008, Spring 2010, Spring 2011, Spring 2012, spring 2012 - acreditation, Spring 2013, Spring 2014, Spring 2015, Spring 2016, Spring 2017, spring 2018, Spring 2019, Spring 2020, Spring 2021, Spring 2022, Spring 2023, Spring 2024, Spring 2025.

M2110 Linear Algebra and Geometry II

Faculty of Science
Spring 2008
Extent and Intensity
2/2/0. 4 credit(s) (fasci plus compl plus > 4). Recommended Type of Completion: zk (examination). Other types of completion: z (credit).
Teacher(s)
doc. RNDr. Martin Čadek, CSc. (lecturer)
Ing. Mgr. Dávid Dereník (seminar tutor)
doc. RNDr. Jiří Kaďourek, CSc. (seminar tutor)
doc. Mgr. Ondřej Klíma, Ph.D. (seminar tutor)
Guaranteed by
doc. RNDr. Martin Čadek, CSc.
Department of Mathematics and Statistics – Departments – Faculty of Science
Timetable
Thu 15:00–16:50 U-aula
  • Timetable of Seminar Groups:
M2110/01: Mon 14:00–15:50 UP1, J. Kaďourek
M2110/02: Thu 17:00–18:50 UP1, D. Dereník
M2110/03: Wed 10:00–11:50 N41, O. Klíma
M2110/04: Tue 8:00–9:50 UP2, O. Klíma
M2110/05: Tue 10:00–11:50 UP2, O. Klíma
Prerequisites
M1110 Linear Algebra I || M1111 Linear Algebra I ||( FI:MB003 Linear Algebra and Geometry I )
Knowledege of basic notion of linear algebra is supposed.
Course Enrolment Limitations
The course is also offered to the students of the fields other than those the course is directly associated with.
fields of study / plans the course is directly associated with
there are 11 fields of study the course is directly associated with, display
Course objectives
The aim of this second course in linear algebra is to introduce other basic notions such as affine and projective spaces, bilinear and quadratic forms, eingenvalues and eigenvectors of linear operators. In more details the spaces with scalar product and properties of orthogonal and selfadjoint operators are examined. All is applied in affine and Euclidean geometry. At the end we deal with the Jordan canonical form.
Syllabus
  • Affine geometry: affine spaces and subspaces, affine geometry and affine mappings. Linear forms: dual space, dual basis, dual homomorphism. Bilinear and quadratic forms: definition, matrix with respect to given basis, diagonalization, signature. Euklidean geometry: orthogonal projection, distance and deviation of affine subspaces. Linear operators: invariant subspaces, eigenvalues and eigen vectors, charakteristic polynomial, algebraic and geometric multiplicity of eigenvalues, conditions for diagonalization. Ortogonal a unitar operators: definition and basic properties, eigenvalues, geometric meaning. Self adjoint operators: adjoint operator, symmetric and hermitian matrices, spectral decomposition. Jordan canonical form: nilpotent endomorphisms, root subspaces, computations.
Literature
  • Zlatoš P.: Lineárna algebra a geometria, připravovaná skripta MFF Univerzity Komenského v Bratislavě, elektronicky dostupné na http://www.math.muni.cz/pub/math/people/Paseka/lectures/LA/
  • Slovák, Jan. Lineární algebra. Učební texty. Brno:~Masarykova univerzita, 1998. 138. elektronicky dostupné na http://www.math.muni.cz/~slovak.
Assessment methods (in Czech)
Výuka: přednáška a klasická cvičení. Zkouška: písemná a ústní. Ke zkoušce je nutný zápočet ze cvičení.
Language of instruction
Czech
Follow-Up Courses
Further comments (probably available only in Czech)
Study Materials
Information on completion of the course: ukončení zápočtem možné pouze rozhodnutím učitele
The course is taught annually.
Credit evaluation note: 2 kr. zápočet.
Listed among pre-requisites of other courses
Teacher's information
http://www.math.muni.cz/~cadek
The course is also listed under the following terms Spring 2008 - for the purpose of the accreditation, Spring 2011 - only for the accreditation, Spring 2000, Spring 2001, Spring 2002, Spring 2003, Spring 2004, Spring 2005, Spring 2006, Spring 2007, Spring 2009, Spring 2010, Spring 2011, Spring 2012, spring 2012 - acreditation, Spring 2013, Spring 2014, Spring 2015, Spring 2016, Spring 2017, spring 2018, Spring 2019, Spring 2020, Spring 2021, Spring 2022, Spring 2023, Spring 2024, Spring 2025.

M2110 Linear Algebra and Geometry II

Faculty of Science
Spring 2007
Extent and Intensity
2/2/0. 4 credit(s) (plus 2 credits for an exam). Recommended Type of Completion: zk (examination). Other types of completion: z (credit).
Teacher(s)
doc. RNDr. Martin Čadek, CSc. (lecturer)
doc. RNDr. Jiří Kaďourek, CSc. (seminar tutor)
doc. Mgr. Ondřej Klíma, Ph.D. (seminar tutor)
RNDr. Jan Vondra, Ph.D. (assistant)
Guaranteed by
doc. RNDr. Martin Čadek, CSc.
Department of Mathematics and Statistics – Departments – Faculty of Science
Contact Person: doc. RNDr. Martin Čadek, CSc.
Timetable
Thu 12:00–13:50 U-aula
  • Timetable of Seminar Groups:
M2110/01: Mon 15:00–16:50 UP1, J. Kaďourek
M2110/03: Thu 8:00–9:50 UP1, O. Klíma
M2110/04: Wed 10:00–11:50 UP1, O. Klíma
M2110/05: Wed 8:00–9:50 UP1, O. Klíma
Prerequisites
M1110 Linear Algebra I ||( FI:MB003 Linear Algebra and Geometry I )
Knowledege of basic notion of linear algebra is supposed.
Course Enrolment Limitations
The course is also offered to the students of the fields other than those the course is directly associated with.
fields of study / plans the course is directly associated with
there are 11 fields of study the course is directly associated with, display
Course objectives
The aim of this second course in linear algebra is to introduce other basic notions such as affine and projective spaces, bilinear and quadratic forms, eingenvalues and eigenvectors of linear operators. In more details the spaces with scalar product and properties of orthogonal and selfadjoint operators are examined. All is applied in affine and Euclidean geometry. At the end we deal with the Jordan canonical form.
Syllabus
  • Affine geometry: affine spaces and subspaces, affine geometry and affine mappings. Linear forms: dual space, dual basis, dual homomorphism. Bilinear and quadratic forms: definition, matrix with respect to given basis, diagonalization, signature. Euklidean geometry: orthogonal projection, distance and deviation of affine subspaces. Linear operators: invariant subspaces, eigenvalues and eigen vectors, charakteristic polynomial, algebraic and geometric multiplicity of eigenvalues, conditions for diagonalization. Ortogonal a unitar operators: definition and basic properties, eigenvalues, geometric meaning. Self adjoint operators: adjoint operator, symmetric and hermitian matrices, spectral decomposition. Jordan canonical form: nilpotent endomorphisms, root subspaces, computations.
Literature
  • Zlatoš P.: Lineárna algebra a geometria, připravovaná skripta MFF Univerzity Komenského v Bratislavě, elektronicky dostupné na http://www.math.muni.cz/pub/math/people/Paseka/lectures/LA/
  • Slovák, Jan. Lineární algebra. Učební texty. Brno:~Masarykova univerzita, 1998. 138. elektronicky dostupné na http://www.math.muni.cz/~slovak.
Assessment methods (in Czech)
Výuka: přednáška a klasická cvičení. Zkouška: písemná a ústní. Ke zkoušce je nutný zápočet ze cvičení.
Language of instruction
Czech
Follow-Up Courses
Further comments (probably available only in Czech)
Information on completion of the course: ukončení zápočtem možné pouze rozhodnutím učitele
The course is taught annually.
Credit evaluation note: 2 kr. zápočet.
Listed among pre-requisites of other courses
Teacher's information
http://www.math.muni.cz/~cadek
The course is also listed under the following terms Spring 2008 - for the purpose of the accreditation, Spring 2011 - only for the accreditation, Spring 2000, Spring 2001, Spring 2002, Spring 2003, Spring 2004, Spring 2005, Spring 2006, Spring 2008, Spring 2009, Spring 2010, Spring 2011, Spring 2012, spring 2012 - acreditation, Spring 2013, Spring 2014, Spring 2015, Spring 2016, Spring 2017, spring 2018, Spring 2019, Spring 2020, Spring 2021, Spring 2022, Spring 2023, Spring 2024, Spring 2025.

M2110 Linear Algebra and Geometry II

Faculty of Science
Spring 2006
Extent and Intensity
2/2/0. 4 credit(s) (fasci plus compl plus > 4). Type of Completion: zk (examination).
Teacher(s)
doc. RNDr. Martin Čadek, CSc. (lecturer)
doc. Mgr. Ondřej Klíma, Ph.D. (seminar tutor)
Mgr. Michaela Vokřínková (seminar tutor)
RNDr. Jan Vondra, Ph.D. (seminar tutor)
Guaranteed by
doc. RNDr. Martin Čadek, CSc.
Department of Mathematics and Statistics – Departments – Faculty of Science
Contact Person: doc. RNDr. Martin Čadek, CSc.
Timetable
Wed 15:00–16:50 U-aula
  • Timetable of Seminar Groups:
M2110/01: Wed 11:00–12:50 UP2, M. Vokřínková
M2110/02: Wed 9:00–10:50 UP2, M. Vokřínková
M2110/03: Wed 11:00–12:50 UP1, O. Klíma
M2110/04: Wed 9:00–10:50 UP1, O. Klíma
M2110/05: Thu 14:00–15:50 UP1, J. Vondra
Prerequisites
M1110 Linear Algebra I ||( FI:MB003 Linear Algebra and Geometry I )
Knowledege of basic notion of linear algebra is supposed.
Course Enrolment Limitations
The course is also offered to the students of the fields other than those the course is directly associated with.
fields of study / plans the course is directly associated with
there are 11 fields of study the course is directly associated with, display
Course objectives
The aim of this second course in linear algebra is to introduce other basic notions such as affine and projective spaces, bilinear and quadratic forms, eingenvalues and eigenvectors of linear operators. In more details the spaces with scalar product and properties of orthogonal and selfadjoint operators are examined. All is applied in affine and Euclidean geometry. At the end we deal with the Jordan canonical form.
Syllabus
  • Affine geometry: affine spaces and subspaces, affine geometry and affine mappings. Linear forms: dual space, dual basis, dual homomorphism. Bilinear and quadratic forms: definition, matrix with respect to given basis, diagonalization, signature. Euklidean geometry: orthogonal projection, distance and deviation of affine subspaces. Linear operators: invariant subspaces, eigenvalues and eigen vectors, charakteristic polynomial, algebraic and geometric multiplicity of eigenvalues, conditions for diagonalization. Ortogonal a unitar operators: definition and basic properties, eigenvalues, geometric meaning. Self adjoint operators: adjoint operator, symmetric and hermitian matrices, spectral decomposition. Jordan canonical form: nilpotent endomorphisms, root subspaces, computations.
Literature
  • Zlatoš P.: Lineárna algebra a geometria, připravovaná skripta MFF Univerzity Komenského v Bratislavě, elektronicky dostupné na http://www.math.muni.cz/pub/math/people/Paseka/lectures/LA/
  • Slovák, Jan. Lineární algebra. Učební texty. Brno:~Masarykova univerzita, 1998. 138. elektronicky dostupné na http://www.math.muni.cz/~slovak.
Assessment methods (in Czech)
Výuka: přednáška a klasická cvičení. Zkouška: písemná a ústní. Ke zkoušce je nutný zápočet ze cvičení.
Language of instruction
Czech
Follow-Up Courses
Further comments (probably available only in Czech)
Study Materials
The course is taught annually.
Listed among pre-requisites of other courses
Teacher's information
http://www.math.muni.cz/~cadek
The course is also listed under the following terms Spring 2008 - for the purpose of the accreditation, Spring 2011 - only for the accreditation, Spring 2000, Spring 2001, Spring 2002, Spring 2003, Spring 2004, Spring 2005, Spring 2007, Spring 2008, Spring 2009, Spring 2010, Spring 2011, Spring 2012, spring 2012 - acreditation, Spring 2013, Spring 2014, Spring 2015, Spring 2016, Spring 2017, spring 2018, Spring 2019, Spring 2020, Spring 2021, Spring 2022, Spring 2023, Spring 2024, Spring 2025.

M2110 Linear Algebra and Geometry II

Faculty of Science
Spring 2005
Extent and Intensity
2/2/0. 4 credit(s) (fasci plus compl plus > 4). Type of Completion: zk (examination).
Teacher(s)
doc. RNDr. Martin Čadek, CSc. (lecturer)
doc. Mgr. Jaroslav Hrdina, Ph.D. (seminar tutor)
Mgr. David Kruml, Ph.D. (seminar tutor)
RNDr. Jan Vondra, Ph.D. (seminar tutor)
doc. Mgr. Lenka Zalabová, Ph.D. (seminar tutor)
Guaranteed by
doc. RNDr. Martin Čadek, CSc.
Department of Mathematics and Statistics – Departments – Faculty of Science
Contact Person: doc. RNDr. Martin Čadek, CSc.
Timetable
Thu 14:00–15:50 U-aula
  • Timetable of Seminar Groups:
M2110/01: Mon 16:00–17:50 UP2, D. Kruml
M2110/02: Wed 12:00–13:50 UM, J. Hrdina
M2110/03: Mon 8:00–9:50 UP2, J. Hrdina
M2110/04: Thu 16:00–17:50 UM, L. Zalabová
M2110/05: Thu 12:00–13:50 U1, J. Vondra
Prerequisites
M1110 Linear Algebra I
Knowledege of basic notion of linear algebra is supposed.
Course Enrolment Limitations
The course is also offered to the students of the fields other than those the course is directly associated with.
fields of study / plans the course is directly associated with
there are 7 fields of study the course is directly associated with, display
Course objectives
The aim of this second course in linear algebra is to introduce other basic notions such as affine and projective spaces, bilinear and quadratic forms, eingenvalues and eigenvectors of linear operators. In more details the spaces with scalar product and properties of orthogonal and selfadjoint operators are examined. All is applied in affine and Euclidean geometry. At the end we deal with the Jordan canonical form.
Syllabus
  • Affine geometry: affine spaces and subspaces, affine geometry and affine mappings. Linear forms: dual space, dual basis, dual homomorphism. Bilinear and quadratic forms: definition, matrix with respect to given basis, diagonalization, signature. Euklidean geometry: orthogonal projection, distance and deviation of affine subspaces. Linear operators: invariant subspaces, eigenvalues and eigen vectors, charakteristic polynomial, algebraic and geometric multiplicity of eigenvalues, conditions for diagonalization. Ortogonal a unitar operators: definition and basic properties, eigenvalues, geometric meaning. Self adjoint operators: adjoint operator, symmetric and hermitian matrices, spectral decomposition. Jordan canonical form: nilpotent endomorphisms, root subspaces, computations.
Literature
  • Zlatoš P.: Lineárna algebra a geometria, připravovaná skripta MFF Univerzity Komenského v Bratislavě, elektronicky dostupné na http://www.math.muni.cz/pub/math/people/Paseka/lectures/LA/
  • Slovák, Jan. Lineární algebra. Učební texty. Brno:~Masarykova univerzita, 1998. 138. elektronicky dostupné na http://www.math.muni.cz/~slovak.
Assessment methods (in Czech)
Výuka: přednáška a klasická cvičení. Zkouška: písemná a ústní. Ke zkoušce je nutný zápočet ze cvičení.
Language of instruction
Czech
Follow-Up Courses
Further comments (probably available only in Czech)
Study Materials
The course is taught annually.
Listed among pre-requisites of other courses
Teacher's information
http://www.math.muni.cz/~cadek
The course is also listed under the following terms Spring 2008 - for the purpose of the accreditation, Spring 2011 - only for the accreditation, Spring 2000, Spring 2001, Spring 2002, Spring 2003, Spring 2004, Spring 2006, Spring 2007, Spring 2008, Spring 2009, Spring 2010, Spring 2011, Spring 2012, spring 2012 - acreditation, Spring 2013, Spring 2014, Spring 2015, Spring 2016, Spring 2017, spring 2018, Spring 2019, Spring 2020, Spring 2021, Spring 2022, Spring 2023, Spring 2024, Spring 2025.

M2110 Linear Algebra and Geometry II

Faculty of Science
Spring 2004
Extent and Intensity
2/2/0. 4 credit(s) (fasci plus compl plus > 4). Type of Completion: zk (examination).
Teacher(s)
doc. RNDr. Martin Čadek, CSc. (lecturer)
doc. Mgr. Ondřej Klíma, Ph.D. (seminar tutor)
doc. Mgr. Vojtěch Žádník, Ph.D. (seminar tutor)
Guaranteed by
doc. RNDr. Martin Čadek, CSc.
Department of Mathematics and Statistics – Departments – Faculty of Science
Contact Person: doc. RNDr. Martin Čadek, CSc.
Timetable
Thu 14:00–15:50 aula Údolní
  • Timetable of Seminar Groups:
M2110/01: No timetable has been entered into IS. M. Čadek
M2110/02: Mon 9:00–10:50 UK, O. Klíma
M2110/03: Mon 11:00–12:50 UK, O. Klíma
M2110/04: Mon 16:00–17:50 U1, V. Žádník
Prerequisites
M1110 Linear Algebra I
Knowledege of basic notion of linear algebra is supposed.
Course Enrolment Limitations
The course is also offered to the students of the fields other than those the course is directly associated with.
fields of study / plans the course is directly associated with
Course objectives
The aim of this second course in linear algebra is to introduce other basic notions such as affine and projective spaces, bilinear and quadratic forms, eingenvalues and eigenvectors of linear operators. In more details the spaces with scalar product and properties of orthogonal and selfadjoint operators are examined. All is applied in affine and Euclidean geometry. At the end we deal with the Jordan canonical form.
Syllabus
  • Affine geometry: affine spaces and subspaces, affine geometry and affine mappings. Linear forms: dual space, dual basis, dual homomorphism. Bilinear and quadratic forms: definition, matrix with respect to given basis, diagonalization, signature. Euklidean geometry: orthogonal projection, distance and deviation of affine subspaces. Linear operators: invariant subspaces, eigenvalues and eigen vectors, charakteristic polynomial, algebraic and geometric multiplicity of eigenvalues, conditions for diagonalization. Ortogonal a unitar operators: definition and basic properties, eigenvalues, geometric meaning. Self adjoint operators: adjoint operator, symmetric and hermitian matrices, spectral decomposition. Jordan canonical form: nilpotent endomorphisms, root subspaces, computations.
Literature
  • Zlatoš P.: Lineárna algebra a geometria, připravovaná skripta MFF Univerzity Komenského v Bratislavě, elektronicky dostupné na http://www.math.muni.cz/pub/math/people/Paseka/lectures/LA/
  • Slovák, Jan. Lineární algebra. Učební texty. Brno:~Masarykova univerzita, 1998. 138. elektronicky dostupné na http://www.math.muni.cz/~slovak.
Assessment methods (in Czech)
Výuka: přednáška a klasická cvičení. Zkouška: písemná a ústní. Ke zkoušce je nutný zápočet ze cvičení.
Language of instruction
Czech
Follow-Up Courses
Further comments (probably available only in Czech)
The course is taught annually.
Listed among pre-requisites of other courses
Teacher's information
http://www.math.muni.cz/~cadek
The course is also listed under the following terms Spring 2008 - for the purpose of the accreditation, Spring 2011 - only for the accreditation, Spring 2000, Spring 2001, Spring 2002, Spring 2003, Spring 2005, Spring 2006, Spring 2007, Spring 2008, Spring 2009, Spring 2010, Spring 2011, Spring 2012, spring 2012 - acreditation, Spring 2013, Spring 2014, Spring 2015, Spring 2016, Spring 2017, spring 2018, Spring 2019, Spring 2020, Spring 2021, Spring 2022, Spring 2023, Spring 2024, Spring 2025.

M2110 Linear Algebra and Geometry II

Faculty of Science
Spring 2003
Extent and Intensity
2/2/0. 4 credit(s) (fasci plus compl plus > 4). Recommended Type of Completion: zk (examination). Other types of completion: k (colloquium).
Teacher(s)
doc. RNDr. Martin Čadek, CSc. (lecturer)
RNDr. Jarmila Elbelová, Ph.D. (seminar tutor)
Mgr. Michal Fikera (seminar tutor)
Guaranteed by
doc. RNDr. Martin Čadek, CSc.
Department of Mathematics and Statistics – Departments – Faculty of Science
Contact Person: doc. RNDr. Martin Čadek, CSc.
Timetable of Seminar Groups
M2110/01: No timetable has been entered into IS. M. Fikera
M2110/02: No timetable has been entered into IS. J. Elbelová
M2110/03: No timetable has been entered into IS. J. Elbelová
Prerequisites
M1110 Linear Algebra I
Knowledege of basic notion of linear algebra is supposed.
Course Enrolment Limitations
The course is also offered to the students of the fields other than those the course is directly associated with.
fields of study / plans the course is directly associated with
Course objectives
The aim of this second course in linear algebra is to introduce other basic notions such as affine and projective spaces, bilinear and quadratic forms, eingenvalues and eigenvectors of linear operators. In more details the spaces with scalar product and properties of orthogonal and selfadjoint operators are examined. All is applied in affine and Euclidean geometry and in classification of quadrics. At the end we deal with the Jordan canonical form.
Syllabus
  • Affine geometry: affine spaces and subspaces, affine geometry and affine mappings. Bilinear and quadratic forms: definition, matrix with respect to given basis, diagonalization, signature,quadrics and their affine classification. Euklidean geometry: orthogonal projection, distance and deviation of affine subspaces. Linear operators: invariant subspaces, eigenvalues and eigen vectors, charakteristic polynomial, algebraic and geometric multiplicity of eigenvalues, conditions for diagonalization. Ortogonal a unitar operators: definition and basic properties, eigenvalues, geometric meaning. Self adjoint operators: adjoint operator, symmetric and hermitian matrices, spectral decomposition, metric classification quadrics. Jordan canonical form: nilpotent endomorphisms, root subspaces, computations.
Literature
  • Zlatoš P.: Lineárna algebra a geometria, připravovaná skripta MFF Univerzity Komenského v Bratislavě, elektronicky dostupné na http://www.math.muni.cz/pub/math/people/Paseka/lectures/LA/
  • Slovák, Jan. Lineární algebra. Učební texty. Brno:~Masarykova univerzita, 1998. 138. elektronicky dostupné na http://www.math.muni.cz/~slovak.
Assessment methods (in Czech)
Výuka: přednáška a klasická cvičení. Zkouška: písemná a ústní.
Language of instruction
Czech
Further comments (probably available only in Czech)
Information on completion of the course: Studenti programu matematika a aplikovaná matematika si musejí zapsat zkoušku.
The course is taught annually.
Listed among pre-requisites of other courses
Teacher's information
http://www.math.muni.cz/~cadek
The course is also listed under the following terms Spring 2008 - for the purpose of the accreditation, Spring 2011 - only for the accreditation, Spring 2000, Spring 2001, Spring 2002, Spring 2004, Spring 2005, Spring 2006, Spring 2007, Spring 2008, Spring 2009, Spring 2010, Spring 2011, Spring 2012, spring 2012 - acreditation, Spring 2013, Spring 2014, Spring 2015, Spring 2016, Spring 2017, spring 2018, Spring 2019, Spring 2020, Spring 2021, Spring 2022, Spring 2023, Spring 2024, Spring 2025.

M2110 Linear algebra II

Faculty of Science
Spring 2002
Extent and Intensity
3/2/0. 8 credit(s). Type of Completion: zk (examination).
Teacher(s)
doc. RNDr. Josef Niederle, CSc. (lecturer)
doc. Mgr. Vojtěch Žádník, Ph.D. (seminar tutor)
Guaranteed by
prof. RNDr. Jan Paseka, CSc.
Department of Mathematics and Statistics – Departments – Faculty of Science
Contact Person: doc. RNDr. Josef Niederle, CSc.
Prerequisites (in Czech)
M1110 Linear algebra I
Course Enrolment Limitations
The course is also offered to the students of the fields other than those the course is directly associated with.
fields of study / plans the course is directly associated with
Syllabus (in Czech)
  • Bilineární, kvadradické a hermitovské formy
  • Afinní klasifikace kuželoseček
  • Skalární součin, euklidovské a unitární prostory
  • Euklidovská geometrie
  • Vlastní čísla a vlastní vektory
  • Jordanův kanonický tvar
  • Ortogonální a unitární operátory
  • Samoadjungované operátory a jejich vlstní čísla
  • Věta o hlavních osách, metrická klasifikace kuželoseček
  • Lineární grupy
  • Projektivní prostory
Language of instruction
Czech
Further comments (probably available only in Czech)
The course is taught annually.
The course is taught: every week.
Listed among pre-requisites of other courses
The course is also listed under the following terms Spring 2008 - for the purpose of the accreditation, Spring 2011 - only for the accreditation, Spring 2000, Spring 2001, Spring 2003, Spring 2004, Spring 2005, Spring 2006, Spring 2007, Spring 2008, Spring 2009, Spring 2010, Spring 2011, Spring 2012, spring 2012 - acreditation, Spring 2013, Spring 2014, Spring 2015, Spring 2016, Spring 2017, spring 2018, Spring 2019, Spring 2020, Spring 2021, Spring 2022, Spring 2023, Spring 2024, Spring 2025.

M2110 Linear algebra II

Faculty of Science
Spring 2001
Extent and Intensity
3/2/0. 8 credit(s). Type of Completion: zk (examination).
Teacher(s)
doc. RNDr. Pavol Zlatoš, CSc. (lecturer)
prof. RNDr. Jan Paseka, CSc. (seminar tutor)
Guaranteed by
doc. RNDr. Pavol Zlatoš, CSc.
Department of Mathematics and Statistics – Departments – Faculty of Science
Contact Person: doc. RNDr. Pavol Zlatoš, CSc.
Prerequisites (in Czech)
M1110 Linear Algebra I
Course Enrolment Limitations
The course is also offered to the students of the fields other than those the course is directly associated with.
fields of study / plans the course is directly associated with
Course objectives (in Czech)
1.Analytická geometrie I, afinní prostory. Afinní prostory Rn a Cn a jejich podprostory, obecné vlastnosti, řešení základních úloh. 2.Prostory se skalárním součinem. (Skalární součin, ortogonalita, Grammův-Schmidtův ortogonalizační proces, unitární a ortogonální zobrazení. 3.Analytická geometrie II, euklidovské prostory. Bodové euklidovské prostory, standardní úlohy, odchylky podprostorů. 4.Lineární a kvadratické formy. Duální vektorový prostor, duální báze, bilineární a multilineární zobrazení, vlastnosti bilineárních a kvadratických forem, hermitovské formy. 5.Spektrální teorie. Základní vlastnosti samoadjungovaných a idempotentních zobrazení, ortogonální klasifikace kvadratických forem. 6.Analytická geometrie III, aplikace. Determinant, orientace a objem, kuželosečky a kvadriky, projektivní rozšíření. 7.Kanonické tvary. Diskuse různých kanonických tvarů, vybrané aplikace. Vhodná rozšíření a dodatky (pokryto elektronickými učebními texty): Ad 4. Rozklad na vlastní a kořenové podprostory, geometrické odvození Jordanova kanonického tvaru endomorfismu, komplexifikace reálných vektorových prostorů a lineárních zobrazení. Ad 9. Diskuse dalších typů zobrazení a odpovídajících matic. Ad 11. Algebraický přístup k Jordanovu kanonickému tvaru. Tenzory. Tenzory jako multilineární zobrazení, tenzorový součin, symetrické a antisymetrické tenzory, vnější tenzorový součin.
Language of instruction
Czech
Further Comments
The course is taught annually.
The course is taught: every week.
Listed among pre-requisites of other courses
The course is also listed under the following terms Spring 2008 - for the purpose of the accreditation, Spring 2011 - only for the accreditation, Spring 2000, Spring 2002, Spring 2003, Spring 2004, Spring 2005, Spring 2006, Spring 2007, Spring 2008, Spring 2009, Spring 2010, Spring 2011, Spring 2012, spring 2012 - acreditation, Spring 2013, Spring 2014, Spring 2015, Spring 2016, Spring 2017, spring 2018, Spring 2019, Spring 2020, Spring 2021, Spring 2022, Spring 2023, Spring 2024, Spring 2025.

M2110 Linear algebra II

Faculty of Science
Spring 2000
Extent and Intensity
3/2/0. 8 credit(s). Type of Completion: zk (examination).
Teacher(s)
prof. RNDr. Jan Slovák, DrSc. (lecturer)
Guaranteed by
prof. RNDr. Jan Slovák, DrSc.
Department of Mathematics and Statistics – Departments – Faculty of Science
Contact Person: prof. RNDr. Jan Slovák, DrSc.
Prerequisites (in Czech)
M1110 Linear algebra I
Course Enrolment Limitations
The course is also offered to the students of the fields other than those the course is directly associated with.
fields of study / plans the course is directly associated with
Syllabus (in Czech)
  • 1.Analytická geometrie I, afinní prostory. Afinní prostory Rn a Cn a jejich podprostory, obecné vlastnosti, řešení základních úloh. 2.Prostory se skalárním součinem. (Skalární součin, ortogonalita, Grammův-Schmidtův ortogonalizační proces, unitární a ortogonální zobrazení. 3.Analytická geometrie II, euklidovské prostory. Bodové euklidovské prostory, standardní úlohy, odchylky podprostorů. 4.Lineární a kvadratické formy. Duální vektorový prostor, duální báze, bilineární a multilineární zobrazení, vlastnosti bilineárních a kvadratických forem, hermitovské formy. 5.Spektrální teorie. Základní vlastnosti samoadjungovaných a idempotentních zobrazení, ortogonální klasifikace kvadratických forem. 6.Analytická geometrie III, aplikace. Determinant, orientace a objem, kuželosečky a kvadriky, projektivní rozšíření. 7.Kanonické tvary. Diskuse různých kanonických tvarů, vybrané aplikace. Vhodná rozšíření a dodatky (pokryto elektronickými učebními texty): Ad 4. Rozklad na vlastní a kořenové podprostory, geometrické odvození Jordanova kanonického tvaru endomorfismu, komplexifikace reálných vektorových prostorů a lineárních zobrazení. Ad 9. Diskuse dalších typů zobrazení a odpovídajících matic. Ad 11. Algebraický přístup k Jordanovu kanonickému tvaru. Tenzory. Tenzory jako multilineární zobrazení, tenzorový součin, symetrické a antisymetrické tenzory, vnější tenzorový součin.
Language of instruction
Czech
Further Comments
The course is taught annually.
The course is taught: every week.
Listed among pre-requisites of other courses
The course is also listed under the following terms Spring 2008 - for the purpose of the accreditation, Spring 2011 - only for the accreditation, Spring 2001, Spring 2002, Spring 2003, Spring 2004, Spring 2005, Spring 2006, Spring 2007, Spring 2008, Spring 2009, Spring 2010, Spring 2011, Spring 2012, spring 2012 - acreditation, Spring 2013, Spring 2014, Spring 2015, Spring 2016, Spring 2017, spring 2018, Spring 2019, Spring 2020, Spring 2021, Spring 2022, Spring 2023, Spring 2024, Spring 2025.

M2110 Linear Algebra and Geometry II

Faculty of Science
spring 2012 - acreditation

The information about the term spring 2012 - acreditation is not made public

Extent and Intensity
2/2/0. 4 credit(s) (příf plus uk k 1 zk 2 plus 1 > 4). Recommended Type of Completion: zk (examination). Other types of completion: z (credit).
Teacher(s)
doc. RNDr. Martin Čadek, CSc. (lecturer)
Ing. Mgr. Dávid Dereník (seminar tutor)
doc. RNDr. Jiří Kaďourek, CSc. (seminar tutor)
doc. Mgr. Ondřej Klíma, Ph.D. (seminar tutor)
Guaranteed by
doc. RNDr. Martin Čadek, CSc.
Department of Mathematics and Statistics – Departments – Faculty of Science
Supplier department: Department of Mathematics and Statistics – Departments – Faculty of Science
Prerequisites
M1110 Linear Algebra I || M1111 Linear Algebra I ||( FI:MB003 Linear Algebra and Geometry I )
Knowledege of basic notion of linear algebra is supposed.
Course Enrolment Limitations
The course is also offered to the students of the fields other than those the course is directly associated with.
fields of study / plans the course is directly associated with
there are 12 fields of study the course is directly associated with, display
Course objectives
The aim of this second course in linear algebra is to introduce other basic notions of linear algebra. Passing the course the stuidents *will know affine spaces, bilinear and quadratic forms, eingenvalues and eigenvectors of linear operators, *they will be able to solve problems concerning the spaces with scalar product and properties of orthogonal and selfadjoint operators and *to find the Jordan canonical form.
Syllabus
  • Affine geometry: affine spaces and subspaces, affine geometry and affine mappings. Linear forms: dual space, dual basis, dual homomorphism. Bilinear and quadratic forms: definition, matrix with respect to given basis, diagonalization, signature. Euklidean geometry: orthogonal projection, distance and deviation of affine subspaces. Linear operators: invariant subspaces, eigenvalues and eigen vectors, charakteristic polynomial, algebraic and geometric multiplicity of eigenvalues, conditions for diagonalization. Ortogonal a unitar operators: definition and basic properties, eigenvalues, geometric meaning. Self adjoint operators: adjoint operator, symmetric and hermitian matrices, spectral decomposition. Jordan canonical form: nilpotent endomorphisms, root subspaces, computations.
Literature
  • Zlatoš P.: Lineárna algebra a geometria, připravovaná skripta MFF Univerzity Komenského v Bratislavě, elektronicky dostupné na http://www.math.muni.cz/pub/math/people/Paseka/lectures/LA/
  • Slovák, Jan. Lineární algebra. Učební texty. Brno:~Masarykova univerzita, 1998. 138. elektronicky dostupné na http://www.math.muni.cz/~slovak.
Teaching methods
Lectures and exercises (tutorials).
Assessment methods
Exam: witten and oral. Requirements to the exam: to obtain 50% of points from tests written during semester.
Language of instruction
Czech
Follow-Up Courses
Further comments (probably available only in Czech)
Information on completion of the course: ukončení zápočtem možné pouze rozhodnutím učitele
The course is taught annually.
The course is taught: every week.
Credit evaluation note: 2 kr. zápočet.
Listed among pre-requisites of other courses
Teacher's information
http://www.math.muni.cz/~cadek
The course is also listed under the following terms Spring 2008 - for the purpose of the accreditation, Spring 2011 - only for the accreditation, Spring 2000, Spring 2001, Spring 2002, Spring 2003, Spring 2004, Spring 2005, Spring 2006, Spring 2007, Spring 2008, Spring 2009, Spring 2010, Spring 2011, Spring 2012, Spring 2013, Spring 2014, Spring 2015, Spring 2016, Spring 2017, spring 2018, Spring 2019, Spring 2020, Spring 2021, Spring 2022, Spring 2023, Spring 2024, Spring 2025.

M2110 Linear Algebra and Geometry II

Faculty of Science
Spring 2011 - only for the accreditation
Extent and Intensity
2/2/0. 4 credit(s) (příf plus uk k 1 zk 2 plus 1 > 4). Recommended Type of Completion: zk (examination). Other types of completion: z (credit).
Teacher(s)
doc. RNDr. Martin Čadek, CSc. (lecturer)
Ing. Mgr. Dávid Dereník (seminar tutor)
doc. RNDr. Jiří Kaďourek, CSc. (seminar tutor)
doc. Mgr. Ondřej Klíma, Ph.D. (seminar tutor)
Guaranteed by
doc. RNDr. Martin Čadek, CSc.
Department of Mathematics and Statistics – Departments – Faculty of Science
Prerequisites
M1110 Linear algebra I || M1111 Linear Algebra I ||( FI:MB003 Linear Algebra and Geometry I )
Knowledege of basic notion of linear algebra is supposed.
Course Enrolment Limitations
The course is also offered to the students of the fields other than those the course is directly associated with.
fields of study / plans the course is directly associated with
there are 12 fields of study the course is directly associated with, display
Course objectives
The aim of this second course in linear algebra is to introduce other basic notions of linear algebra. Passing the course the stuidents *will know affine spaces, bilinear and quadratic forms, eingenvalues and eigenvectors of linear operators, *they will be able to solve problems concerning the spaces with scalar product and properties of orthogonal and selfadjoint operators and *to find the Jordan canonical form.
Syllabus
  • Affine geometry: affine spaces and subspaces, affine geometry and affine mappings. Linear forms: dual space, dual basis, dual homomorphism. Bilinear and quadratic forms: definition, matrix with respect to given basis, diagonalization, signature. Euklidean geometry: orthogonal projection, distance and deviation of affine subspaces. Linear operators: invariant subspaces, eigenvalues and eigen vectors, charakteristic polynomial, algebraic and geometric multiplicity of eigenvalues, conditions for diagonalization. Ortogonal a unitar operators: definition and basic properties, eigenvalues, geometric meaning. Self adjoint operators: adjoint operator, symmetric and hermitian matrices, spectral decomposition. Jordan canonical form: nilpotent endomorphisms, root subspaces, computations.
Literature
  • Zlatoš P.: Lineárna algebra a geometria, připravovaná skripta MFF Univerzity Komenského v Bratislavě, elektronicky dostupné na http://www.math.muni.cz/pub/math/people/Paseka/lectures/LA/
  • Slovák, Jan. Lineární algebra. Učební texty. Brno:~Masarykova univerzita, 1998. 138. elektronicky dostupné na http://www.math.muni.cz/~slovak.
Teaching methods
Lectures and exercises (tutorials).
Assessment methods
Exam: witten and oral. Requirements to the exam: to obtain internal credit from exercises.
Language of instruction
Czech
Follow-Up Courses
Further comments (probably available only in Czech)
Information on completion of the course: ukončení zápočtem možné pouze rozhodnutím učitele
The course is taught annually.
The course is taught: every week.
Credit evaluation note: 2 kr. zápočet.
Listed among pre-requisites of other courses
Teacher's information
http://www.math.muni.cz/~cadek
The course is also listed under the following terms Spring 2008 - for the purpose of the accreditation, Spring 2000, Spring 2001, Spring 2002, Spring 2003, Spring 2004, Spring 2005, Spring 2006, Spring 2007, Spring 2008, Spring 2009, Spring 2010, Spring 2011, Spring 2012, spring 2012 - acreditation, Spring 2013, Spring 2014, Spring 2015, Spring 2016, Spring 2017, spring 2018, Spring 2019, Spring 2020, Spring 2021, Spring 2022, Spring 2023, Spring 2024, Spring 2025.

M2110 Linear Algebra and Geometry II

Faculty of Science
Spring 2008 - for the purpose of the accreditation
Extent and Intensity
2/2/0. 4 credit(s) (fasci plus compl plus > 4). Recommended Type of Completion: zk (examination). Other types of completion: z (credit).
Teacher(s)
doc. RNDr. Martin Čadek, CSc. (lecturer)
doc. RNDr. Jiří Kaďourek, CSc. (seminar tutor)
doc. Mgr. Ondřej Klíma, Ph.D. (seminar tutor)
Guaranteed by
doc. RNDr. Martin Čadek, CSc.
Department of Mathematics and Statistics – Departments – Faculty of Science
Contact Person: doc. RNDr. Martin Čadek, CSc.
Prerequisites
M1110 Linear algebra I ||( FI:MB003 Linear Algebra and Geometry I )
Knowledege of basic notion of linear algebra is supposed.
Course Enrolment Limitations
The course is also offered to the students of the fields other than those the course is directly associated with.
fields of study / plans the course is directly associated with
there are 11 fields of study the course is directly associated with, display
Course objectives
The aim of this second course in linear algebra is to introduce other basic notions such as affine and projective spaces, bilinear and quadratic forms, eingenvalues and eigenvectors of linear operators. In more details the spaces with scalar product and properties of orthogonal and selfadjoint operators are examined. All is applied in affine and Euclidean geometry. At the end we deal with the Jordan canonical form.
Syllabus
  • Affine geometry: affine spaces and subspaces, affine geometry and affine mappings. Linear forms: dual space, dual basis, dual homomorphism. Bilinear and quadratic forms: definition, matrix with respect to given basis, diagonalization, signature. Euklidean geometry: orthogonal projection, distance and deviation of affine subspaces. Linear operators: invariant subspaces, eigenvalues and eigen vectors, charakteristic polynomial, algebraic and geometric multiplicity of eigenvalues, conditions for diagonalization. Ortogonal a unitar operators: definition and basic properties, eigenvalues, geometric meaning. Self adjoint operators: adjoint operator, symmetric and hermitian matrices, spectral decomposition. Jordan canonical form: nilpotent endomorphisms, root subspaces, computations.
Literature
  • Zlatoš P.: Lineárna algebra a geometria, připravovaná skripta MFF Univerzity Komenského v Bratislavě, elektronicky dostupné na http://www.math.muni.cz/pub/math/people/Paseka/lectures/LA/
  • Slovák, Jan. Lineární algebra. Učební texty. Brno:~Masarykova univerzita, 1998. 138. elektronicky dostupné na http://www.math.muni.cz/~slovak.
Assessment methods (in Czech)
Výuka: přednáška a klasická cvičení. Zkouška: písemná a ústní. Ke zkoušce je nutný zápočet ze cvičení.
Language of instruction
Czech
Follow-Up Courses
Further comments (probably available only in Czech)
Information on completion of the course: ukončení zápočtem možné pouze rozhodnutím učitele
The course is taught annually.
The course is taught: every week.
Credit evaluation note: 2 kr. zápočet.
Listed among pre-requisites of other courses
Teacher's information
http://www.math.muni.cz/~cadek
The course is also listed under the following terms Spring 2011 - only for the accreditation, Spring 2000, Spring 2001, Spring 2002, Spring 2003, Spring 2004, Spring 2005, Spring 2006, Spring 2007, Spring 2008, Spring 2009, Spring 2010, Spring 2011, Spring 2012, spring 2012 - acreditation, Spring 2013, Spring 2014, Spring 2015, Spring 2016, Spring 2017, spring 2018, Spring 2019, Spring 2020, Spring 2021, Spring 2022, Spring 2023, Spring 2024, Spring 2025.
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