M504 Linear Algebra and Geometry II

Faculty of Informatics
Spring 2002
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)
Mgr. Michal Bulant, Ph.D. (lecturer)
prof. RNDr. Jan Paseka, CSc. (lecturer)
Guaranteed by
doc. RNDr. Jiří Kaďourek, CSc.
Departments – Faculty of Science
Contact Person: prof. RNDr. Jan Paseka, CSc.
Timetable
Tue 14:00–15:50 UKP, Thu 15:00–16:50 D1
Prerequisites
M503 Linear Algebra and Geometry I && (! M004 Linear Algebra and Geometry II )&&(! NOW ( 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
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
  • Zlatoš, Pavol. Lineárna algebra a geometria. Předběžné učební texty MFF UK v Bratislavě.
  • Slovák, Jan. Lineární algebra. Učební texty. Brno:~Masarykova univerzita, 1998. 138. elektronicky dostupné na http://www.math.muni.cz/~slovak.
  • 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.
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 2000, Spring 2001, Spring 2003.
  • Enrolment Statistics (Spring 2002, recent)
  • Permalink: https://is.muni.cz/course/fi/spring2002/M504