Linearni ohranjevalci komutativnosti

magistrsko delo

Gordana Radić (Author), Tatjana Petek (Mentor)

Abstract

Linearni ohranjevalci komutativnosti na matrični algebri so tesno povezani s preslikavami, ki vse matrike ranga 1 preslikajo v matrike ranga 1. Zato najprej določimo obliko linearnih preslikav, ki ohranjajo rang 1, nato pa natančno opišemo ne singularne linearne preslikave na algebri kvadratnih matrik z elementi iz algebraično zaprtega polja F s karakteristiko 0. Z močnejšo predpostavko, da preslikava ohranja komutativnost v obe smeri, vendar sedaj brez predpostavke surjektivnosti, dobimo podoben rezultat. Linearne preslikave, ki ohranjajo komutativnost oziroma ohranjajo komutativnost v obe smeri, proučimo tudi na algebri zgoraj trikotnih matrik nad poljubnim poljem in na realni (jordanski) algebri hermitskih kompleksnih matrik. V slednjem primeru dobimo karakterizacijo celo brez predpostavke surjektivnosti in z ohranjanjem komutativnosti samo v eno smer.

Keywords

linearna preslikava;ohranjanje ranga;ohranjanje komutativnosti;hermitske matrike;zgoraj trikotne matrike;magistrska dela;

Data

Language:	Slovenian
Year of publishing:	2014
Typology:	2.09 - Master's Thesis
Organization:	UM FNM - Faculty of Natural Sciences and Mathematics
Publisher:	[G. Radić]
UDC:	512.645.5(043.2)
COBISS:	20454152
Views:	1601
Downloads:	111
Average score:	0 (0 votes)
Metadata:

Other data

Secondary language:	English
Secondary title:	Linear commutativity preservers
Secondary abstract:	Linear commutativity-preservers on matrix algebra are linked to linear maps which map every rank-one matrix to a rank-one matrix. So, firstly we develope the structure of linear maps that preserve rank 1. After that we describe all non-singular linear maps on the algebra of all square matrices over an algebraically closed field F with characteristic 0. Furthermore, by modifying the hypothesis and leaving out the non-singularity, we arrive to the similar conclusion. In this case, the stronger assumption is needed, which is preserving commutativity in both directions. We also consider linear maps that preserve commutativity in one or in both directions on the algebra of all upper-triangular matrices over any field and on the real (jordan) algebra of all complex self-adjoint matrices. In second case, the characterization is obtained without non-singularity assumption and preserving commutativity in one direction only.
Secondary keywords:	linear maps;rank preserving maps;commutativity preserving maps;hermitian matrices;upper triangular matrices;theses;
URN:	URN:SI:UM:
Type (COBISS):	Master's thesis
Thesis comment:	Univ. v Mariboru, Fak. za naravoslovje in matematiko, Oddelek za matematiko in računalništvo
Pages:	XIV, 100 str.
ID:	8728978