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FI:MA004 Linear Algebra and Geometry II - Course Information

## MA004 Linear Algebra and Geometry II

**Faculty of Informatics**

Spring 2005

**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)**- doc. RNDr. Martin Čadek, CSc. (lecturer)
**Guaranteed by**- doc. RNDr. Martin Čadek, CSc.

Faculty of Informatics

Contact Person: doc. RNDr. Martin Čadek, CSc. **Timetable**- Thu 14:00–15:50 U5
**Prerequisites**- !
**M004**Linear Algebra and Geometry II

Knowledge of basic notions of linear algebra is supposed. **Course Enrolment Limitations**- The course is only offered to the students of the study fields 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 such as affine 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**- Slovák, Jan.
*Lineární algebra*. Učební texty. Brno:~Masarykova univerzita,1998. 138. elektronicky dostupné nahttp://www.math.muni.cz/~slovak . - Zlatoš, Pavol. Lineárna algebra a geometria. Předběžné učební texty MFF UK v Bratislavě.

- Slovák, Jan.
**Assessment methods**(in Czech)- Početní a teoretické zvládnutí přednesené látky (porozumnění základním pojmům a větám, jednoduché důkazy).
**Language of instruction**- Czech
**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/~slovak http://www.math.muni.cz/~cadek

- Enrolment Statistics (recent)

- Permalink: https://is.muni.cz/course/fi/spring2005/MA004