Linear Algebra A2

Garant předmětu:

Lecturer:

Tutor:

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 corresponding matrix theory.

Requirements:

Having passed the subject LAP.

Syllabus of lectures:

Inverse matrix and operator. Permutation and determinant. Spectral theory (eigenvalue, eigenvector, diagonalization). Hermitian and quadratic forms. Scalar product and orthogonality. Metric geometry. Riesz theorem and adjoint operator.

Syllabus of tutorials:

1. Gauss method of determination of inverse matrix. 2. Different methods of determinant calculation. 3. Evaluation of eigenvalues and eigenvectors, diagonalization. 4. Canonical transformation of a quadratic form, determination of character of the form and signature. 5. Examples of scalar products, Gram-Schmidt orthogonalization, orthonormal basis. 6. Metric geometry -- calculation of distance and angles.

7. Riesz theorem and adjoint operator. Characterization of normal operators and their spectrum.

Study Objective:

Knowledge: Mastering of the concepts of theory of linear operators and matrices, especially in spaces equiped with a scalar product, and applications of linear algebra in metric geometry.

Skills:

Ability to use these findings in further studies not only in mathematical disciplines, but also in physics, economics etc.

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:

Further information:

http://kmlinux.fjfi.cvut.cz/~balkolub/vyuka.html

No time-table has been prepared for this course

The course is a part of the following study plans:

• BS Matematické inženýrství - Matematické modelování (compulsory course of the specialization)
• BS Matematické inženýrství - Matematická fyzika (compulsory course of the specialization)
• BS Matematické inženýrství - Aplikované matematicko-stochastické metody (compulsory elective course)
• BS Informatická fyzika (compulsory elective course)
• BS Dozimetrie a aplikace ionizujícího záření (compulsory elective course)
• BS Experimentální jaderná a částicová fyzika (compulsory elective course)
• BS Inženýrství pevných látek (compulsory elective course)
• BS Diagnostika materiálů (compulsory elective course)
• BS Fyzika a technika termojaderné fúze (compulsory elective course)
• BS Fyzikální elektronika (compulsory elective course)