na študijskem programu 2. stopnje Izobraževalna matematika - dvopredmetna
Sanja Levart (Author), Mateja Grašič (Mentor)

Abstract

Cilj magistrskega dela je predstaviti nekaj rezultatov, ki povezujejo zapis matrik v obliki matričnega komutatorja s kakšno posebno lastnostjo matrike. Velja na primer, da je matrika A, ki zadošča kateremu od pogojev a) A[A,B]=[A,B]A za neko matriko B b) [adj(A),B]=A za neko matriko B c) [A,B]=A za neko matriko B nilpotentna in da je sled matrike enaka 0 natanko tedaj, ko lahko to matriko predstavimo v obliki nekega matričnega komutatorja.

Keywords

magistrska dela;matrika;matrični komutator;nilpotentna matrika;sled matrike;

Data

Language: Slovenian
Year of publishing:
Typology: 2.09 - Master's Thesis
Organization: UM FNM - Faculty of Natural Sciences and Mathematics
Publisher: [S. Levart]
UDC: 512.643.12(043.2)
COBISS: 17715459 Link will open in a new window
Views: 502
Downloads: 39
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Other data

Secondary language: English
Secondary title: Matrix commutators
Secondary abstract: The aim of the master's thesis is to present some results that relate the matrix property in the form of some matrix commutator condition to some specific property of this matrix. For example, for the matrix A that satisfies any of the conditions: a) A[A,B] = [A,B]A for some matrix B b) [adj(A),B] = A for some matrix B c) [A,B] = A for some matrix B it follows that A is a nilpotent matrix. We also show that the trace of the matrix is 0 if and only if we can represent this matrix in the form of a commutator.
Secondary keywords: master theses;matrix;matrix communicators;nilpotent matrix;trace of matrix;
Type (COBISS): Master's thesis/paper
Thesis comment: Univ. v Mariboru, Fak. za naravoslovje in matematiko, Oddelek za matematiko in računalništvo
Pages: VIII, 32 f.
ID: 11331469
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