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CZECH TECHNICAL UNIVERSITY IN PRAGUE
STUDY PLANS
2022/2023

Advanced Matrix Analysis

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Code Completion Credits Range Language
A8B01AMA Z,ZK 4 3P+1S Czech
Lecturer:
Martin Křepela
Tutor:
Martin Křepela
Supervisor:
Department of Mathematics
Synopsis:

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.

Requirements:
Syllabus of lectures:

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.

Syllabus of tutorials:
Study Objective:
Study materials:

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

2. M. Dont: Maticová analýza, skripta, nakl. ČVUT 2011

Note:
Time-table for winter semester 2022/2023:
Time-table is not available yet
Time-table for summer semester 2022/2023:
06:00–08:0008:00–10:0010:00–12:0012:00–14:0014:00–16:0016:00–18:0018:00–20:0020:00–22:0022:00–24:00
Mon
Tue
roomT2:A4-202a
Křepela M.
14:30–16:00
(lecture parallel1)
Dejvice
Ucebna
Wed
roomT2:A4-203a
Křepela M.
16:15–17:00
(lecture parallel1)
Dejvice
Učebna
roomT2:A4-203a
Křepela M.
17:00–17:45
(lecture parallel1
parallel nr.101)

Dejvice
Učebna
Thu
Fri
The course is a part of the following study plans:
Data valid to 2022-12-05
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