FI:M504 Linear Algebra and Geometry II - Course Information

M504 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)

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 M503 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

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

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
• 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)

Vyžaduje se početní zvládnutí přednesené látky.

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 (recent)
  
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