Matrix theory

Lecturer:

Edita Pelantová (gar.)

Tutor:

Edita Pelantová (gar.)

Supervisor:

Department of Mathematics

Synopsis:

The subject deals mainly with the concept of similarity of matrices over the complex field, with the spectrum of non-negative matrices and with properties of tensor product.

Requirements:

Successful completion of courses Linear algbera and General algebra.

Syllabus of lectures:

1. The Jordan Theorem and transformation of matrix into its canonical form, invariant subspaces.

2. Relation between matrices and graphs, non-negative matrices and the Perron-Frobenius theorem, stochastic matrices.

3. Tensor product of matrices and its properties.

4. Matrices over finite fields.

Syllabus of tutorials:

Study Objective:

Acquired knowledge: fundamental results in theory of canonical form of matrices and the Perron-Frobenius theory for nonnegative matrices.

Acquired skills: applications of these results in the graph theory and in the algebraic number theory.

Study materials:

Obligatory:

[1] M. Fiedler, Special Matrices and Their Applications in Numerical Mathematics. Second Edition. Dover Publications, Inc., Mineola, U.S.A., 2008.

Optional:

[2] D.K. Faddeev, V.N. Faddeeva, Computational methods of linear algebra. Translated by Robert C. Williams W. H. Freeman and Co., San Francisco-London 1963

Note:

Time-table for winter semester 2011/2012:

Time-table is not available yet

Time-table for summer semester 2011/2012:

Time-table is not available yet

The course is a part of the following study plans: