Linear Algebra A2

Grading of the course requires grading of the following courses:

Linear Algebra 1 (01LA1)

Lecturer:

Lubomíra Balková (gar.)

Tutor:

Lubomíra Balková (gar.), Václav Klika

Supervisor:

Department of Mathematics

Synopsis:

The subject is devoted to the theory of linear operators on vector spaces (mainly equipped with scalar product).In the same time we introduce the matrix theory.

Requirements:

LAP.

Syllabus of lectures:

Inverse operator and matrix. Determinant, eigenvalue, eigenvector. Hermitian and quadratic forms - canonical form. Vector spaces with scalar product. Linear operators on vector spaces with scalar product - normal, self-adjoint, isometric. Geometry in Euclidean spaces.

Syllabus of tutorials:

1. Gauss method of evaluation of inverse matrix. 2. Different methods of determinant calculation. 3. Evaluation of eigenvalues and eigenvectors, diagonalizability. 4. Canonical transformation of a quadratic form, determination of character of the form and indices of inertia. 5. Examples of scalar products, Gramm-Schmidt orthogonalization, complete set. 6. Properties of normal operators and their spectra. 7. Geometry in metric spaces - calculation of distances and angles.

Study Objective:

Knowledge: Mastering the concepts s theory of linear operators and matrices, especially in spaces equiped with a scalar product and applications of linear algebra in linear geometry.Skills:To be able to use these findings in further studies not only of mathematical disciplines,but also in physics,economics.

Study materials:

Key references:

[1] Linear Algebra with Applications, Prentice-Hall, Inc., Englewood Cliffs, New Jersey,1980

[2] C. W. Curtis : Linear Algebra, An Introductory Approach, Springer-Verlag, New York, Berlin, Heidelberg, Tokyo 1984.

Recommended references:

[3] P. Lancaster : Theory of Matrices, Academic Press, New York, London, 1969.

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: