|
|
The course is scheduled for Tuesday at 15:40 in room S9.
Schedule of particular lectures:
| 30.9. | SVD decomposition: the proof and a relation between singular values and eigenvalues. Applications of SVD: orthogonalization, geometric viewpoint on linear mappings, low-rank approximation and compression.
[chapter 3 of the textbook] |
| 7.10. | The Moore-Penrose pseudoinverse matrix and its applications: projection matrix, relation to linear mappings, the least squares method. Drazin pseudoinverzse matrix: definition, properties and an application to matrix groups.
[chapter 4 of the textbook] |
| plan 14.10. | Matrix norms: Vector lp norms on matrices + examples (incl. Frobenius norm), induced matrix norms + examples (incl. spectral norm), geometric interpretation of induced norms, equivalence of matrix norms. Interpretation of singular values as the minimum distance to matrices of smaller ranks.
[sections 5.1 and 5.4 of the textbook] |
| plan 21.10. | Estimation of spectral radius using matrix norm and other relations, Gelfand's formula, estimation of the size of polynomial roots. Convergence of power sequences and series, Neumann series. Orthogonally invariant norms in brief.
[sections 5.2-5.4 of the textbook] |
Literature:
