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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

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

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Page updated 26.2.2021 17:52:17, semester: Z/2020-1, L/2021-2, L/2020-1, Z/2021-2, Send comments about the content to the Administrators of the Academic Programs

Proposal and Realization: I. Halaška (K336), J. Novák (K336)