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CZECH TECHNICAL UNIVERSITY IN PRAGUE
STUDY PLANS
2023/2024

Advanced Matrix Analysis

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

The course covers advanced topics of linear algebra, in particular matrix factorizations and construction of matrix functions.

Requirements:

Good knowledge of fundamental topics of linear algebra and single-variable analysis is a prerequisity. Some of the course topics need implemenation of multivariable analysis concepts (normed spaces, power series). It is thus recommended to complete a multivariable analysis course (MA2) before registering for this course.

Syllabus of lectures:

Main topics:

1. Inner product, norm, norm equivalence in finite-dimenstional spaces.

2. Projectors and othogonal projectors, Gram-Schmidt orthogonalization method, QR factorization.

3. Unitary and orthogonal matrices, Householder reduction.

4. Singular value decompostition.

5. Eigenvalues, eigenvectors and eigenspaces, diagonalization, Cholesky factorization.

6. Schur decomposition, normal and Hermitian matrices.

7. Matrix index, nilpotent matrices.

8. Jordan form of a matrix, spectral projectors.

9. Construction of a matrix function by power series and through the spectral decomposition theorem.

10. Matrix functions as Hermite polynomials, Vandermonde system.

11. Matrix exponential, solutions to systems of linear ODE with constant coefficients.

Possible extenstions:

LU factorization, numerical stability of GEM, least squares.

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 2023/2024:
Time-table is not available yet
Time-table for summer semester 2023/2024:
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 2023-11-30
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