Subject description - A8B01AMA

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A8B01AMA Advanced Matrix Analysis
Roles:P Extent of teaching:3P+1S
Department:13101 Language of teaching:CS
Guarantors:Pták P. Completion:Z,ZK
Lecturers:Pták P. Credits:4
Tutors:Pták P. Semester:L

Anotation:

This is a continuation of linear algebra. A relatively good knowledge of basic notions of linear algebra is supposed. The aim is to explain spectral theorems and their applications. Further Jordan form of a matrix and functions of a matrix are studied.

Course outlines:

1. A recapitulation of basic notions of linear algebra.
2. Real and complex matrices, matrix algebra.
3. Eigenvalues and eigenvectors of square matrices.
4. Diagonalization of a square matrix, conditions of diagonalizability.
5. Standars inner product, orthogonalization, orthogonal projection.
6. Unitary matrices, the Fourier matrix.
7. Eigenvalues and eigenvectors of hermitian and unitary matrices.
8. Spectral theorem for hermitian matrices.
9. Definite matrices, characterization in terms of eigenvalues.
10. Least squares, algebraic formulation, normal equations.
11. Singular value decomposition, application to lest squares.
12. Jordan form of a matrix.
13. Function of a matrix, definition and computation.
14. Power series representation of a matrix function, some application.

Exercises outline:

Literature:

1. C. D. Meyer: Matrix Analysis and Applied Linear Algebra, SIAM 2000
2. M. Dont: Maticová analýza, skripta, nakl. ČVUT 2011

Requirements:

Subject is included into these academic programs:

Program Branch Role Recommended semester
BPOES_2020 Common courses P 4
BPOES Common courses P 4


Page updated 25.5.2020 07:51:48, semester: Z,L/2020-1, Z,L/2019-20, Send comments about the content to the Administrators of the Academic Programs Proposal and Realization: I. Halaška (K336), J. Novák (K336)