20.500.12556/RUP-7732 General preservers of quasi-commutativity Splošni ohranjevalci kvazi-komutativnosti Let ▫$M_n$▫ be the algebra of all ▫$n \times n$▫ matrices over ▫$\mathbb{C}$▫. We say that ▫$A, B \in M_n$▫ quasi-commute if there exists a nonzero ▫$\xi \in \mathbb{C}$▫ such that ▫$AB = \xi BA$▫. In the paper we classify bijective not necessarily linear maps ▫$\Phi \colon M_n \to M_n$▫ which preserve quasi-commutativity in both directions. Naj bo ▫$M_n$▫ algebra vseh ▫$n \times n$▫ matrik nad obsegom ▫$\mathbb{C}$▫. Pravimo, da matriki ▫$A, B \in M_n$▫ kvazi-komutirata, če obstaja tak neničelni skalar ▫$\xi \in \mathbb{C}$▫, da je ▫$AB = \xi BA$▫. V članku klasificiramo bijektivne ne nujno linearne preslikave iz ▫$M_n$▫ v ▫$M_n$▫, ki ohranjajo kvazi-komutativnost v obeh smereh. mathematics linear algebra general preserver matrix algebra quasi-commutativity matematika linearna algebra splošni ohranjevalci matrična algebra kvazi-komutativnost true true false Angleški jezik Slovenski jezik Delo ni kategorizirano 2016-04-08 16:46:54 2017-04-03 08:12:00 2024-03-01 13:33:25 0000-00-00 00:00:00 2010 0 0 str. 758-786 no. 4 Vol. 62 2010 0000-00-00 NiDoloceno NiDoloceno NiDoloceno 0000-00-00 0000-00-00 0000-00-00 0008-414X 512.643 25186816 15627353 http://dx.doi.org/10.4153/CJM-2010-041-x 1 https://repozitorij.upr.si/Dokument.php?lang=slv&id=7732 Inštitut Andrej Marušič 0 0 0