M004 Linear Algebra II

Faculty of Informatics
Spring 1998
Extent and Intensity
3/0. 3 credit(s). Recommended Type of Completion: zk (examination). Other types of completion: k (colloquium), z (credit).
Teacher(s)
doc. RNDr. Martin Čadek, CSc. (lecturer)
Pavol Zlatoš (lecturer)
Guaranteed by
Contact Person: doc. RNDr. Martin Čadek, CSc.
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
The course is also listed under the following terms Spring 1996, Spring 1997, Spring 1999, Spring 2000, Spring 2001, Spring 2002.
  • Enrolment Statistics (Spring 1998, recent)
  • Permalink: https://is.muni.cz/course/fi/spring1998/M004