MA004 Linear Algebra and Geometry II

Faculty of Informatics
Spring 2003
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
there are 6 fields of study the course is directly associated with, display
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
The course is also listed under the following terms Spring 2004, Spring 2005.
  • Enrolment Statistics (Spring 2003, recent)
  • Permalink: https://is.muni.cz/course/fi/spring2003/MA004