# Subject description - A8B01AMA

Summary of Study | Summary of Branches | All Subject Groups | All Subjects | List of Roles | Explanatory Notes               Instructions
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)