Mathematics 5C

Lecturer:

Tutor:

Supervisor:

Department of Mathematics

Synopsis:

Linear transformations, eigenvalues, eigenvectors. Similar matrices, diagonalizability. Generalized eigenvectors, Jordan canonical form. Bilinear and quadratic forms. Positive definite matrices, symetric matrices. Ortogonality, Schmidt orthogonalization. Functions of matrices, matrix exponencial. Singular value decomposition. Numerical computation of eigenvalues and eigenvectors. Information, entropy, communication channels. Kraft's inequality, McMillan's theorem. Shannon's theorem. Linear codes, Hamming codes. Reed-Muller codes, cyclic codes.

Requirements:

Syllabus of lectures:

1. Linear transformations, eigenvalues, eigenvectors

2. Similar matrices, diagonalizability

3. Generalized eigenvectors, Jordan canonical form

4. Bilinear and quadratic forms

5. Positive definite matrices, symetric matrices

6. Ortogonality, Schmidt orthogonalization

7. Functions of matrices, matrix exponencial

8. Singular value decomposition

9. Numerical computation of eigenvalues and eigenvectors

10. Information, entropy, communication channels

11. Kraft's inequality, McMillan's theorem

12. Shannon's theorem

13. Linear codes, Hamming codes

14. Reed-Muller codes, cyclic codes

Syllabus of tutorials:

1. Linear transformations, eigenvalues, eigenvectors

2. Similar matrices, diagonalizability

3. Generalized eigenvectors, Jordan canonical form

4. Bilinear and quadratic forms

5. Positive definite matrices, symetric matrices

6. Ortogonality, Schmidt orthogonalization

7. Functions of matrices, matrix exponencial

8. Singular value decomposition

9. Numerical computation of eigenvalues and eigenvectors

10. Information, entropy, communication channels

11. Kraft's inequality, McMillan's theorem

12. Shannon's theorem

13. Linear codes, Hamming codes

14. Reed-Muller codes, cyclic codes

Study Objective:

Study materials:

[1] C. D. Meyer: Matrix Analysis and Applied Linear Algebra. SIAM, 2000.

Note:

Further information:

No time-table has been prepared for this course

The course is a part of the following study plans:

• Kybernetika a měření-bakalářský blok (compulsory course)
• Kybernetika a měření-bakalářský blok (compulsory course)