M004 Linear Algebra and Geometry II

Faculty of Informatics
Spring 2002
Extent and Intensity
2/0. 2 credit(s) (plus extra credits for completion). Recommended Type of Completion: zk (examination). Other types of completion: k (colloquium), z (credit).
Teacher(s)
Mgr. Michal Bulant, Ph.D. (lecturer)
prof. RNDr. Jan Paseka, CSc. (lecturer)
Guaranteed by
doc. RNDr. Jiří Kaďourek, CSc.
Departments – Faculty of Science
Contact Person: prof. RNDr. Jan Paseka, CSc.
Timetable
Tue 14:00–15:50 UKP, Thu 15:00–16:50 D1
Prerequisites
M003 Linear Algebra and Geometry I && (! M504 Linear Algebra and Geometry II )&&(!NOW( M504 Linear Algebra and Geometry II ))
Prerequisites M003 Linear Algebra and Geometry 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
  • Bilinear and quadratic forms: Definitions, description of bilinear forms in coordinates, symmetric bilinear forms and symmetric matrices, diagonalization of quadratic forms, quadrics. x
  • Spaces with scalar product: Scalar product, ortogonal vectors, Gramm--Schmidt process, unitary and ortogonal matrices, ortogonal projection.
  • Analytic geometry in Euklidean spaces: Distances and angles between afine Euklidean subspaces.
  • Linear operators: Invariant subspaces, eigenvectors and eigenvalues, spectrum of linear operator, basic information on Jordan canonical forms.
  • Spectral theory: Definition and properties of selfadjoint linear operators, their spectrum and eigenvalues, ortogonal classification of quadratic forms.
  • Linear and affine groups: Linear groups $GL(n,R)$, $GL(n,C)$, $SL(n,R)$, $O(n)$, $SO(n)$ and their affine extensions. /SYLTEXT>
Literature
  • Slovák, Jan. Lineární algebra. Učební texty. Brno:~Masarykova univerzita,1998. 138. elektronicky dostupné na http://www.math.muni.cz/~slovak.
  • Zlatoš, Pavol. Lineárna algebra a geometria. Předběžné učební texty MFF UK v Bratislavě.
  • ŠMARDA, Bohumil. Lineární algebra. Praha: Státní pedagogické nakladatelství, 1985, 159 s. info
Assessment methods (in Czech)
Početní a teoretické zvládnutí přednesené látky (porozumnění základním pojmům a větám, jednoduché důkazy).
Language of instruction
Czech
Further Comments
The course is taught annually.
Teacher's information
http://www.math.muni.cz/~slovak http://www.math.muni.cz/~cadek
The course is also listed under the following terms Spring 1996, Spring 1997, Spring 1998, Spring 1999, Spring 2000, Spring 2001.

M004 Linear Algebra and Geometry II

Faculty of Informatics
Spring 2001
Extent and Intensity
3/0. 3 credit(s) (plus extra credits for completion). Recommended Type of Completion: zk (examination). Other types of completion: k (colloquium), z (credit).
Teacher(s)
doc. RNDr. Martin Čadek, CSc. (lecturer)
Mgr. Milan Sekanina, Ph.D. (lecturer)
Guaranteed by
doc. RNDr. Jiří Kaďourek, CSc.
Departments – Faculty of Science
Contact Person: doc. RNDr. Martin Čadek, CSc.
Timetable
Mon 9:00–11:50 D1, Tue 7:00–9:50 D1
Prerequisites
M003 Linear Algebra and Geometry I && (! M504 Linear Algebra and Geometry II )
Prerequisites M003 Linear Algebra and Geometry 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
  • Bilinear and quadratic forms: Definitions, description of bilinear forms in coordinates, symmetric bilinear forms and symmetric matrices, diagonalization of quadratic forms, quadrics. x
  • Spaces with scalar product: Scalar product, ortogonal vectors, Gramm--Schmidt process, unitary and ortogonal matrices, ortogonal projection.
  • Analytic geometry in Euklidean spaces: Distances and angles between afine Euklidean subspaces.
  • Linear operators: Invariant subspaces, eigenvectors and eigenvalues, spectrum of linear operator, basic information on Jordan canonical forms.
  • Spectral theory: Definition and properties of selfadjoint linear operators, their spectrum and eigenvalues, ortogonal classification of quadratic forms.
  • Linear and affine groups: Linear groups $GL(n,R)$, $GL(n,C)$, $SL(n,R)$, $O(n)$, $SO(n)$ and their affine extensions. /SYLTEXT>
Literature
  • Slovák, Jan. Lineární algebra. Učební texty. Brno:~Masarykova univerzita,1998. 138. elektronicky dostupné na http://www.math.muni.cz/~slovak.
  • ŠMARDA, Bohumil. Lineární algebra. Praha: Státní pedagogické nakladatelství, 1985, 159 s. info
Assessment methods (in Czech)
Početní a teoretické zvládnutí přednesené látky (porozumnění základním pojmům a větám, jednoduché důkazy). Zkouška se skládá z písemného testu uprostřed semestru s váhou 25 %, který není možné opakovat, z písemky ve zkouškovém období, kterou je možno jedenkrát opakovat, a z případného ústního zkoušení.
Language of instruction
Czech
Further Comments
The course is taught annually.
Teacher's information
http://www.math.muni.cz/~slovak http://www.math.muni.cz/~cadek
The course is also listed under the following terms Spring 1996, Spring 1997, Spring 1998, Spring 1999, Spring 2000, Spring 2002.

M004 Linear Algebra and Geometry II

Faculty of Informatics
Spring 2000
Extent and Intensity
3/0. 3 credit(s) (plus extra credits for completion). Recommended Type of Completion: zk (examination). Other types of completion: k (colloquium), z (credit).
Teacher(s)
doc. RNDr. Martin Čadek, CSc. (lecturer)
Mgr. Milan Sekanina, Ph.D. (lecturer)
Guaranteed by
prof. RNDr. Jan Slovák, DrSc.
Departments – Faculty of Science
Contact Person: doc. RNDr. Martin Čadek, CSc.
Prerequisites
M003 Linear Algebra and Geometry I
Prerequisites M003 Linear Algebra and Geometry 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
  • Bilinear and quadratic forms: Definitions, description of bilinear forms in coordinates, symmetric bilinear forms and symmetric matrices, diagonalization of quadratic forms, quadrics. x
  • Spaces with scalar product: Scalar product, ortogonal vectors, Gramm--Schmidt process, unitary and ortogonal matrices, ortogonal projection.
  • Analytic geometry in Euklidean spaces: Distances and angles between afine Euklidean subspaces.
  • Linear operators: Invariant subspaces, eigenvectors and eigenvalues, spectrum of linear operator, basic information on Jordan canonical forms.
  • Spectral theory: Definition and properties of selfadjoint linear operators, their spectrum and eigenvalues, ortogonal classification of quadratic forms.
  • Linear and affine groups: Linear groups $GL(n,R)$, $GL(n,C)$, $SL(n,R)$, $O(n)$, $SO(n)$ and their affine extensions. /SYLTEXT>
Literature
  • Slovák, Jan. Lineární algebra. Učební texty. Brno:~Masarykova univerzita,1998. 138. elektronicky dostupné na http://www.math.muni.cz/~slovak.
  • ŠMARDA, Bohumil. Lineární algebra. Praha: Státní pedagogické nakladatelství, 1985, 159 s. info
Assessment methods (in Czech)
Početní a teoretické zvládnutí přednesené látky (porozumnění základním pojmům a větám, jednoduché důkazy). Zkouška se skládá z písemného testu uprostřed semestru s váhou 25 %, který není možné opakovat, z písemky ve zkouškovém období, kterou je možno jedenkrát opakovat, a z případného ústního zkoušení.
Language of instruction
Czech
Further Comments
The course is taught annually.
The course is taught: every week.
Teacher's information
http://www.math.muni.cz/~slovak http://www.math.muni.cz/~cadek
The course is also listed under the following terms Spring 1996, Spring 1997, Spring 1998, Spring 1999, Spring 2001, Spring 2002.

M004 Linear Algebra II

Faculty of Informatics
Spring 1999
Extent and Intensity
3/0. 3 credit(s). Recommended Type of Completion: zk (examination). Other types of completion: k (colloquium), z (credit).
Teacher(s)
doc. RNDr. Martin Čadek, CSc. (lecturer)
Milan Sekanina (lecturer)
Guaranteed by
Contact Person: doc. RNDr. Martin Čadek, CSc.
Prerequisites
M003 Linear Algebra I
Prerequsites M003 Linear Algebra and Geometry 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
  • Bilinear and quadratic forms: Definitions, description of bilinear forms in coordinates, symmetric bilinear forms and symmetric matrices, diagonalization of quadratic forms, quadrics. x
  • Spaces with scalar product: Scalar product, ortogonal vectors, Gramm--Schmidt process, unitary and ortogonal matrices, ortogonal projection.
  • Analytic geometry in Euklidean spaces: Distances and angles between afine Euklidean subspaces.
  • Linear operators: Invariant subspaces, eigenvectors and eigenvalues, spectrum of linear operator, basic information on Jordan canonical forms.
  • Spectral theory: Definition and properties of selfadjoint linear operators, their spectrum and eigenvalues, ortogonal classification of quadratic forms.
  • Linear and affine groups: Linear groups $GL(n,R)$, $GL(n,C)$, $SL(n,R)$, $O(n)$, $SO(n)$ and their affine extensions. /SYLTEXT>
Language of instruction
Czech
Further Comments
The course is taught annually.
The course is taught: every week.
Teacher's information
http://www.math.muni.cz/~slovak
The course is also listed under the following terms Spring 1996, Spring 1997, Spring 1998, Spring 2000, Spring 2001, Spring 2002.

M004 Linear Algebra II

Faculty of Informatics
Spring 1998
Extent and Intensity
3/0. 3 credit(s). Recommended Type of Completion: zk (examination). Other types of completion: k (colloquium), z (credit).
Teacher(s)
doc. RNDr. Martin Čadek, CSc. (lecturer)
Pavol Zlatoš (lecturer)
Guaranteed by
Contact Person: doc. RNDr. Martin Čadek, CSc.
Prerequisites
Prerequsites M003 Linear Algebra and Geometry 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
  • Bilinear and quadratic forms: Definitions, description of bilinear forms in coordinates, symmetric bilinear forms and symmetric matrices, diagonalization of quadratic forms, quadrics. x
  • Spaces with scalar product: Scalar product, ortogonal vectors, Gramm--Schmidt process, unitary and ortogonal matrices, ortogonal projection.
  • Analytic geometry in Euklidean spaces: Distances and angles between afine Euklidean subspaces.
  • Linear operators: Invariant subspaces, eigenvectors and eigenvalues, spectrum of linear operator, basic information on Jordan canonical forms.
  • Spectral theory: Definition and properties of selfadjoint linear operators, their spectrum and eigenvalues, ortogonal classification of quadratic forms.
  • Linear and affine groups: Linear groups $GL(n,R)$, $GL(n,C)$, $SL(n,R)$, $O(n)$, $SO(n)$ and their affine extensions. /SYLTEXT>
Language of instruction
Czech
Teacher's information
http://www.math.muni.cz/~slovak
The course is also listed under the following terms Spring 1996, Spring 1997, Spring 1999, Spring 2000, Spring 2001, Spring 2002.

M004 Linear Algebra and Geometry II

Faculty of Informatics
Spring 1997
Extent and Intensity
3/0. 3 credit(s). Recommended Type of Completion: zk (examination). Other types of completion: k (colloquium), z (credit).
Teacher(s)
doc. RNDr. Martin Čadek, CSc. (lecturer)
Guaranteed by
Contact Person: doc. RNDr. Martin Čadek, CSc.
Prerequisites
Prerequsites M003 Linear Algebra and Geometry 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
  • Bilinear and quadratic forms: Definitions, description of bilinear forms in coordinates, symmetric bilinear forms and symmetric matrices, diagonalization of quadratic forms, quadrics. x
  • Spaces with scalar product: Scalar product, ortogonal vectors, Gramm--Schmidt process, unitary and ortogonal matrices, ortogonal projection.
  • Analytic geometry in Euklidean spaces: Distances and angles between afine Euklidean subspaces.
  • Linear operators: Invariant subspaces, eigenvectors and eigenvalues, spectrum of linear operator, basic information on Jordan canonical forms.
  • Spectral theory: Definition and properties of selfadjoint linear operators, their spectrum and eigenvalues, ortogonal classification of quadratic forms.
  • Linear and affine groups: Linear groups $GL(n,R)$, $GL(n,C)$, $SL(n,R)$, $O(n)$, $SO(n)$ and their affine extensions. /SYLTEXT>
Language of instruction
Czech
Teacher's information
http://www.math.muni.cz/~slovak
The course is also listed under the following terms Spring 1996, Spring 1998, Spring 1999, Spring 2000, Spring 2001, Spring 2002.

M004 Linear Algebra and Geometry II

Faculty of Informatics
Spring 1996
Extent and Intensity
0/0. 2 credit(s). Recommended Type of Completion: zk (examination). Other types of completion: k (colloquium), z (credit).
Teacher(s)
prof. RNDr. Jan Slovák, DrSc. (lecturer)
Guaranteed by
Contact Person: prof. RNDr. Jan Slovák, DrSc.
Prerequisites
Prerequsites M003 Linear Algebra and Geometry 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
  • Bilinear and quadratic forms: Definitions, description of bilinear forms in coordinates, symmetric bilinear forms and symmetric matrices, diagonalization of quadratic forms, quadrics. x
  • Spaces with scalar product: Scalar product, ortogonal vectors, Gramm--Schmidt process, unitary and ortogonal matrices, ortogonal projection.
  • Analytic geometry in Euklidean spaces: Distances and angles between afine Euklidean subspaces.
  • Linear operators: Invariant subspaces, eigenvectors and eigenvalues, spectrum of linear operator, basic information on Jordan canonical forms.
  • Spectral theory: Definition and properties of selfadjoint linear operators, their spectrum and eigenvalues, ortogonal classification of quadratic forms.
  • Linear and affine groups: Linear groups $GL(n,R)$, $GL(n,C)$, $SL(n,R)$, $O(n)$, $SO(n)$ and their affine extensions. /SYLTEXT>
Language of instruction
Czech
Teacher's information
http://www.math.muni.cz/~slovak
The course is also listed under the following terms Spring 1997, Spring 1998, Spring 1999, Spring 2000, Spring 2001, Spring 2002.
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