FI:MA004 Linear Algebra and Geometry II - Course Information

MA004 Linear Algebra and Geometry II

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)
RNDr. Jarmila Elbelová, Ph.D. (seminar tutor)

Guaranteed by

doc. RNDr. Martin Čadek, CSc.
Faculty of Informatics
Contact Person: doc. RNDr. Martin Čadek, CSc.

Prerequisites

! M004 Linear Algebra and Geometry II
Prerequisites M003 Linear Algebra and Geometry I

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

• Applied Informatics (programme FI, N-AP)
• Informatics (programme FI, M-IN)
• Informatics (programme FI, N-IN)
• Upper Secondary School Teacher Training in Informatics (programme FI, M-IN)
• Upper Secondary School Teacher Training in Informatics (programme FI, M-SS)
• Upper Secondary School Teacher Training in Informatics (programme FI, N-SS)

Course objectives (in Czech)

Pokračování kurzu Lineární algebra a geometrie I. Pozornost je věnována geometrii Euklidovských a afinních prostorů. Dále jsou probírána zobrazení mezi těmito prostory a vlastnosti matic, které tato zobrazení prezentují.

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.
The course is taught: every week.

Teacher's information

http://www.math.muni.cz/~slovak http://www.math.muni.cz/~cadek

• Enrolment Statistics (Spring 2003, recent)
  
• Permalink: https://is.muni.cz/course/fi/spring2003/MA004