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 1 - 7 / 7  1  1.General preservers of quasi-commutativity on hermitian matricesBojan Kuzma, Gregor Dolinar, 2008, original scientific articleAbstract: Let ▫$H_n$▫ be the set of all ▫$n \times n$▫ hermitian matrices over ▫$\mathbb{C}$▫, ▫$n \ge 3$▫. It is said that ▫$A,B \in H_n$▫ quasi-commute if there exists a nonzero ▫$\xi \in \mathbb{C}$▫ such that ▫$AB = \xi BA$▫ Bijective not necessarily linear maps on hermitian matrices which preserve quasi-commutativity in both directions are classified.Found in: osebiKeywords: mathematics, linear algebra, general preserver, hermitian matrices, quasi-commutativityPublished: 03.04.2017; Views: 848; Downloads: 136 Full text (0,00 KB)This document has more files! More... 2.Bar´ery Gibsona dlja problemy PoliaGregor Dolinar, Bojan Kuzma, Aleksandr Èmilevič Guterman, 2010, published scientific conference contributionAbstract: V članku je obravnavana spodnja meja za število neničelnih elementov v ▫$(0, 1)$▫ matrikah, pri katerem se da permanento vedno pretvoriti v determinanto samo s spreminjanjem predznaka ▫$pm$▫ elementom matrike.Found in: osebiKeywords: matematika, linearna algebra, teorija matrik, permanenta, determinantaPublished: 03.04.2017; Views: 761; Downloads: 23 Full text (0,00 KB)This document has more files! More... 3.General preservers of quasi-commutativity on self-adjoint operatorsBojan Kuzma, Gregor Dolinar, 2010, original scientific articleAbstract: Let ▫$H$▫ be a separable Hilbert space and▫ ${\mathcal B}_{sa}(H)▫$ the set of all bounded linear self-adjoint operators. We say that ▫$A, B \in {\mathcal B}_{sa}(H)$▫ quasi-commute if there exists a nonzero ▫$\xi \in \mathbb{C}$▫ suchthat ▫$AB=\xi BA$▫. Bijective maps on ▫${\mathcal B}_{sa}(H)$▫ which preserve quasi-commutativity in both directions are classified.Found in: osebiKeywords: mathematics, linear algebra, general preserver, self-adjoint operator, quasi-commutativityPublished: 03.04.2017; Views: 833; Downloads: 52 Full text (0,00 KB) 4.General preservers of quasi-commutativityBojan Kuzma, Gregor Dolinar, 2010, original scientific articleAbstract: 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.Found in: osebiKeywords: mathematics, linear algebra, general preserver, matrix algebra, quasi-commutativityPublished: 03.04.2017; Views: 683; Downloads: 54 Full text (0,00 KB) 5.On maximal distances in a commuting graphBojan Kuzma, Polona Oblak, Gregor Dolinar, 2012, original scientific articleAbstract: It is shown that matrices over algebraically closed fields that are farthest apart in the commuting graph must be non-derogatory. Rank-one matrices and diagonalizable matrices are also characterized in terms of the commuting graph.Found in: osebiKeywords: matematika, linearna algebra, teorija grafov, komutirajoči grafi, matrična algebra, algebraično zaprt obseg, centralizator, razdalja v grafih, mathematics, linear algebra, graph theory, commuting graph, matrix algebra, algebraically closed field, centralizer, distance in graphsPublished: 03.04.2017; Views: 856; Downloads: 130 Full text (0,00 KB)This document has more files! More... 6.Permanent versus determinant over a finite fieldGregor Dolinar, Aleksandr Èmilevič Guterman, Marko Orel, Bojan Kuzma, 2013, published scientific conference contributionAbstract: Let ▫$\mathbb{F}$▫ be a finite field of characteristic different from 2. We study the cardinality of sets of matrices with a given determinant or a given permanent for the set of Hermitian matrices ▫$\mathcal{H}_n(\mathbb{F})$▫ and for the whole matrix space ▫$M_n(\mathbb{F})$▫. It is known that for ▫$n = 2$▫, there are bijective linear maps ▫$\Phi$▫ on ▫$\mathcal{H}_n(\mathbb{F})$▫ and ▫$M_n(\mathbb{F})$▫ satisfying the condition per ▫$A = \det \Phi(A)$▫. As an application of the obtained results, we show that if ▫$n \ge 3$▫, then the situation is completely different and already for ▫$n = 3$▫, there is no pair ofmaps ▫$(\Phi, \phi)$▫, where ▫$\Phi$▫ is an arbitrary bijective map on matrices and ▫$\phi \colon \mathbb{F} \to \mathbb{F}$▫ is an arbitrary map such that per ▫$A = \phi(\det \Phi(A))$▫ for all matrices ▫$A$▫ from the spaces ▫$\mathcal{H}_n(\mathbb{F})$▫ and ▫$M_n(\mathbb{F})$▫, respectively. Moreover, for the space ▫$M_n(\mathbb{F})$▫, we show that such a pair of transformations does not exist also for an arbitrary ▫$n > 3$▫ if the field ▫$\mathbb{F}$▫ contains sufficiently many elements (depending on ▫$n$▫). Our results are illustrated by a number of examples.Found in: osebiKeywords: mathematics, linear algebra, matrix theory, permanent, determinantPublished: 03.04.2017; Views: 809; Downloads: 66 Full text (0,00 KB) 7.Maps on self-adjoint operators preserving numerical range of products up to a factorKan He, Gregor Dolinar, Jin Chuan Hou, Bojan Kuzma, 2011, original scientific articleAbstract: Let ▫$H$▫ be a complex Hilbert space and ▫${mathscr{S}}_a(H)$▫ the space of all self adjoint operators on ▫$H$▫. ▫$Phi colon {mathscr{S}}_a(H) to {mathscr{S}}_a(H)$▫ is a surjective map. For ▫$xi, eta in mathbb{C} setminus {1}$▫, then ▫$Phi$▫ satisfies that ▫$$W(AB - xi BA) = W(Phi(A)Phi(B) - etaPhi(B)phi(A))$$▫ for all ▫$A,B in {mathscr{S}}_a(H)$▫ if and only if there exists a unitary operator or con-unitary operator ▫$U$▫ such that ▫$Phi(A) = UAU^ast$▫ for all ▫$A in {mathscr{S}}_a(H)$▫ or ▫$Phi(A) = -UAU^ast$▫ for all ▫$A in {mathscr{S}}_a(H)$▫.Found in: osebiKeywords: matematika, teorija operatorjev, numerični zaklad, ohranjevalciPublished: 03.04.2017; Views: 908; Downloads: 13 Full text (0,00 KB)
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