Linear Algebra B2

Course guarantor:

Lecturer:

Tutor:

Supervisor:

Department of Mathematics

Synopsis:

The subject summarizes the most important notions and theorems related to the matrix theory, to the study of vector spaces with a scalar product and to the linear geometry.

Requirements:

01LALA or 01LALB

Syllabus of lectures:

Matrices and systems of linear algebraic equations - determinants - scalar product and orthogonality - eigenvalues and eigenvectors of matrices - linear geometry in Euclidean space

Syllabus of tutorials:

1. Solving systems of linear algebraic equations

2. Calculation of inverse matrices using the Gauss elimination

3. Permutations and determinants

4. Searching for orthogonal and orthonormal bases, application of the Gram-Schmidt orthogonalization method, calculation of orthogonal projections of vectors

4. Computation of eigenvalues and eigenvectors of matrices

5. Distinct descriptions of linear manifolds and convex sets, computation of intersections of linear manifolds

Study Objective:

Knowledge:

Basic notions from the matrix theory, notions related to the scalar product and the linear geometry from the theoretical point of view.

Abilities:

Application of the knowledge in practical problems.

Study materials:

Key references:

[1] H. G. Campbell, Linear Algebra with Applications, Prentice-Hall, Inc., Englewood Cliffs, New Jersey, 2nd edition, 1980

[2] C.W.Curtis, Linear Algebra, An Introductory Approach, Springer-Verlag, New York, Berlin, Heidelberg, Tokyo, 1974, 4th edition, 1984

Recommended references:

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

Note:

Further information:

No time-table has been prepared for this course

The course is a part of the following study plans: