20.500.12556/DKUM-75590 Matrični komutatorji Matrix commutators 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. 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. matrika matrični komutator nilpotentna matrika sled matrike. matrix matrix commutators nilpotent matrix trace of a matrix. true true false [S. Levart] Slovenski jezik Angleški jezik Magistrsko delo/naloga 2019-12-12 13:21:07 2020-06-09 13:59:32 2022-08-09 11:31:46 2020-06-12 03:12:54 2020 0 Maribor 0 0000-00-00 NiDoloceno NiDoloceno NiDoloceno 0000-00-00 0000-00-00 0000-00-00 512.643.12(043.2) 17715459 URN:SI:UM:DK:V65XJKF9 MAG_Levart_Sanja_2019.pdf MAG_Levart_Sanja_2019.pdf 1 9D8A2B5A9AA430BAE9F4795E7A904EF8 140d7710009a78aae51d24ab308b50a5fc6c0300fcd6a845bf981057d662577c 2b24149f-7c11-11eb-bb7a-00155d0001ca 20.500.12556/dkum/7db79884-40c6-4238-8e07-79acacacdb85 https://dk.um.si/Dokument.php?lang=slv&id=139965 Fakulteta za naravoslovje in matematiko 0 0 0