Linear Algebra B 2

Garant předmětu:

Lecturer:

Tutor:

Supervisor:

Department of Software Engineering

Synopsis:

Determinant. Regular matrix, regular operator. Inverse matrix and operator. Inner product, orthogonality, Gramm-Schmidt orthogonalization process. Linear geometry. Eigenvalues, eigenvectors, diagonalization of matrices. Special types of matrices.

Requirements:

Syllabus of lectures:

1. permutation

2. determinant definition, basic properties

3. cofactor expansion along the row or column

4. use of determinants, Cramer's rule

5. inner product, orthogonal base, Gramm-Schmidt orthogonalization process

6. orthonormal matrix

7. orthogonal complement

8. affine varieties (basic terms)

9. position of affine varieties

10. distance of affine varieties

11. eigenvalue and eigenvector (basic terms)

12. matrix similarity

13. symetric and orthonormal matrices

Syllabus of tutorials:

1. permutation

2. determinant definition, basic properties

3. cofactor expansion along the row or column

4. use of determinants, Cramer's rule

5. inner product, orthogonal base, Gramm-Schmidt orthogonalization process

6. orthonormal matrix

7. orthogonal complement

8. affine varieties (basic terms)

9. position of affine varieties

10. distance of affine varieties

11. eigenvalue and eigenvector (basic terms)

12. matrix similarity

13. symetric and orthonormal matrices

Study Objective:

Knowledge of basic terms of linear algebra.

Ability to prove mathematical theorems and solve problems of linear algebra, especially work with matrices.

Study materials:

Key references:

[1] Dontová, E. Matematika III. Praha: ČVUT, 1999.

[2] Čížková, L. Sbírka příkladů z matematiky I. Praha: ČVUT, 1999.

[3] Study materials and tasks in the MOODLE system (http://moodle.jadernaci.eu).

Recommended references:

[4] Pytlíček, J. Cvičení z algebry a geometrie. Praha: ČVUT, 1997.

Note:

Further information:

No time-table has been prepared for this course

The course is a part of the following study plans: