FI:M004 Linear Algebra and Geometry II

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