M004 Linear Algebra and Geometry II

Faculty of Informatics
Spring 2000
Extent and Intensity
3/0. 3 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)
Mgr. Milan Sekanina, Ph.D. (lecturer)
Guaranteed by
prof. RNDr. Jan Slovák, DrSc.
Departments – Faculty of Science
Contact Person: doc. RNDr. Martin Čadek, CSc.
Prerequisites
M003 Linear Algebra and Geometry I
Prerequisites 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>
Literature
  • 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)
Početní a teoretické zvládnutí přednesené látky (porozumnění základním pojmům a větám, jednoduché důkazy). Zkouška se skládá z písemného testu uprostřed semestru s váhou 25 %, který není možné opakovat, z písemky ve zkouškovém období, kterou je možno jedenkrát opakovat, a z případného ústního zkoušení.
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 1996, Spring 1997, Spring 1998, Spring 1999, Spring 2001, Spring 2002.
  • Enrolment Statistics (Spring 2000, recent)
  • Permalink: https://is.muni.cz/course/fi/spring2000/M004