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:Velebil J. Completion:Z,ZK
Lecturers:Křepela M. Credits:4
Tutors:Křepela M. Semester:L


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

Course outlines:

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.

Exercises outline:


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


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.

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 22.5.2024 05:51:03, semester: Z/2024-5, Z,L/2023-4, Send comments about the content to the Administrators of the Academic Programs Proposal and Realization: I. Halaška (K336), J. Novák (K336)