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
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.