Takagijeva faktorizacija

diplomsko delo

Rebeka Mežan (Author), Marko Slapar (Mentor), Tadej Starčič (Co-mentor)

Abstract

Diplomska naloga Takagijeva faktorizacija bralcu predstavi faktorizacijo kompleksno simetričnih matrik. Kompleksno simetrične matrike v splošnem ne moremo diagonalizirati, lahko pa pokažemo, da so unitarno T-kongruentne diagonalni matriki. Temu rečemo Takagijeva faktorizacija. V prvem poglavju so predstavljene splošne lastnosti matrik ter njihova diagonalizabilnost. Diagonalizacija ni nujno izvedljiva pri kompleksno ortogonalnih matrikah, medtem ko so realno simetrične in kompleksno hermitske matrike vedno diagonalizabilne. Pomemben izrek za razumevanje diagonalizacije in podobnosti je Schurov izrek, ki je v nadaljevanju opisan in dokazan. Kratek del diplomske naloge je posvečen opisu japonskega matematika Teijija Takagija, nato pa sledi glavni del naloge, obravnava Takagijeve faktorizacije.

Keywords

matrike;podobnost matrik;diagonalizacija;Schurov izrek;Takagijeva faktorizacija;

Data

Language:	Slovenian
Year of publishing:	2018
Typology:	2.11 - Undergraduate Thesis
Organization:	UL PEF - Faculty of Education
Publisher:	[R. Mežan]
UDC:	512.643(043.2)
COBISS:	12141385
Views:	544
Downloads:	93
Average score:	0 (0 votes)
Metadata:

Other data

Secondary language:	English
Secondary title:	Takagi factorization
Secondary abstract:	This diploma thesis, Takagi factorization, presents the reader a factorization of complex symmetric matrices. A complex symmetric matrix can not in general be diagonalizable but it can be showed, that it can always be unitary T- congruent to some diagonal matrix. That is called Takagi factorization. In the first chapter the basic properties of matrices and matrix diagonalizability are presented. A diagonalization is not always realisable in the case of a complex orthogonal matrix while for real symmetric and for complex Hermitian matrix the diagonalization always exists. An important theorem for understanding the process of diagonalization and similarity is Schur form. It is described and proved below. Short part of this dissertation is devoted to Japanese mathematician Teiji Takagi, followed by the main subject of this paper, discussion of Takagi factorization.
Secondary keywords:	mathematics;matematika;
File type:	application/pdf
Type (COBISS):	Bachelor thesis/paper
Thesis comment:	Univ. v Ljubljani, Pedagoška fak., Dvopredmetni učitelj
Pages:	26 str.
ID:	10973325