1. Cao, Chongguang; Huang, Liping; Tang, Xiaomin: Additive map preserving rank 2 on alternate matrices. (English).  [J] Afr. Diaspora J. Math 3, No. 2, 107113 (2005). [ISSN 1539845X]Bojan Kuzma, 2006, review, book review, critique Found in: ključnih besedah Summary of found: ...matematika, linear algebra, aditivni ohranjevalec, rang, ... Keywords: matematika, linear algebra, aditivni ohranjevalec, rang Published: 15.10.2013; Views: 1660; Downloads: 8 Full text (0,00 KB) 
2. Jordan triple product homomorphismsBojan Kuzma, 2006, original scientific article Abstract: Nondegenerate mappings that preserve Jordan triple product on ▫${\mathscr{M}}_n({\mathbb{F}}$▫ are characterized. Here, ▫$n \ge 3$▫ and ▫$\mathbb{F}$▫ is an arbitrary field. Found in: ključnih besedah Summary of found: ...mathematics, linear algebra, matrix algebra, Jordan triple product, nonlinear... Keywords: mathematics, linear algebra, matrix algebra, Jordan triple product, nonlinear preserver Published: 15.10.2013; Views: 1641; Downloads: 66 Full text (0,00 KB) 
3. Noninvertibility preservers on Banach algebrasBojan Kuzma, 2006, short scientific article Abstract: It is proved that a linear surjection ▫$\Phi: \mathcal{A} \to \mathcal{B}$▫, which preserves noninvertibility between semisimple, unital, complex Banach algebras, is automatically injective. Found in: ključnih besedah Summary of found: ...It is proved that a linear surjection ▫$\Phi: \mathcal{A} \to \mathcal{B}$▫, which preserves... ...analysis, linear preserver, noninvertible element, semisimple Banach algebra, socle... Keywords: mathematics, functional analysis, linear preserver, noninvertible element, semisimple Banach algebra, socle Published: 15.10.2013; Views: 1262; Downloads: 53 Full text (0,00 KB) 
4. General preservers of quasicommutativity on hermitian matricesBojan Kuzma, Gregor Dolinar, 2008, original scientific article Abstract: Let ▫$H_n$▫ be the set of all ▫$n \times n$▫ hermitian matrices over ▫$\mathbb{C}$▫, ▫$n \ge 3$▫. It is said that ▫$A,B \in H_n$▫ quasicommute if there exists a nonzero ▫$\xi \in \mathbb{C}$▫ such that ▫$AB = \xi BA$▫ Bijective not necessarily linear maps on hermitian matrices which preserve quasicommutativity in both directions are classified. Found in: ključnih besedah Summary of found: ...▫$AB = \xi BA$▫ Bijective not necessarily linear maps on hermitian matrices which preserve quasicommutativity... ...mathematics, linear algebra, general preserver, hermitian matrices, quasicommutativity... Keywords: mathematics, linear algebra, general preserver, hermitian matrices, quasicommutativity Published: 03.04.2017; Views: 668; Downloads: 97 Full text (0,00 KB) This document has more files! More...

5. Additive rankone nonincreasing maps on Hermitian matrices over the field GF(2[sup]2)Marko Orel, Bojan Kuzma, 2009, original scientific article Abstract: A complete classification of additive rankone nonincreasing maps on hermitian matrices over Galois field ▫$GF(2^2)$▫ is obtained. This field is special and was not covered in a previous paper. As a consequence, some known applications, like the classification of additive rankadditivity preserving maps, are extended to arbitrary fields. An application concerning the preservers of hermitian varieties is also presented. Found in: ključnih besedah Summary of found: ...mathematics, linear algebra, additive preserver, hermitian matrices, rank, Galois... Keywords: mathematics, linear algebra, additive preserver, hermitian matrices, rank, Galois field, weak homomorphism of a graph Published: 03.04.2017; Views: 755; Downloads: 26 Full text (0,00 KB) This document has more files! More...

6. General preservers of quasicommutativity on selfadjoint operatorsBojan Kuzma, Gregor Dolinar, 2010, original scientific article Abstract: Let ▫$H$▫ be a separable Hilbert space and▫ ${\mathcal B}_{sa}(H)▫$ the set of all bounded linear selfadjoint operators. We say that ▫$A, B \in {\mathcal B}_{sa}(H)$▫ quasicommute if there exists a nonzero ▫$\xi \in \mathbb{C}$▫ suchthat ▫$AB=\xi BA$▫. Bijective maps on ▫${\mathcal B}_{sa}(H)$▫ which preserve quasicommutativity in both directions are classified. Found in: ključnih besedah Summary of found: ...${\mathcal B}_{sa}(H)▫$ the set of all bounded linear selfadjoint operators. We say that ▫$A, B... ...mathematics, linear algebra, general preserver, selfadjoint operator, quasicommutativity... Keywords: mathematics, linear algebra, general preserver, selfadjoint operator, quasicommutativity Published: 03.04.2017; Views: 690; Downloads: 40 Full text (0,00 KB) 
7. General preservers of quasicommutativityBojan Kuzma, Gregor Dolinar, 2010, original scientific article Abstract: Let ▫$M_n$▫ be the algebra of all ▫$n \times n$▫ matrices over ▫$\mathbb{C}$▫. We say that ▫$A, B \in M_n$▫ quasicommute if there exists a nonzero ▫$\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$▫ which preserve quasicommutativity in both directions. Found in: ključnih besedah Summary of found: ...the paper we classify bijective not necessarily linear maps ▫$\Phi \colon M_n \to M_n$▫ which... ...Let ▫$M_n$▫ be the algebra of all ▫$n \times n$▫ matrices over... Keywords: mathematics, linear algebra, general preserver, matrix algebra, quasicommutativity Published: 03.04.2017; Views: 534; Downloads: 38 Full text (0,00 KB) 
8. On maximal distances in a commuting graphBojan Kuzma, Polona Oblak, Gregor Dolinar, 2012, original scientific article Abstract: It is shown that matrices over algebraically closed fields that are farthest apart in the commuting graph must be nonderogatory. Rankone matrices and diagonalizable matrices are also characterized in terms of the commuting graph. Found in: ključnih besedah Summary of found: ...matematika, linearna algebra, teorija grafov, komutirajoči grafi, matrična algebra,... Keywords: 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 graphs Published: 03.04.2017; Views: 688; Downloads: 86 Full text (0,00 KB) This document has more files! More...

9. Permanent versus determinant over a finite fieldGregor Dolinar, Aleksandr Èmilevič Guterman, Marko Orel, Bojan Kuzma, 2013, published scientific conference contribution Abstract: 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: ključnih besedah Summary of found: ...for ▫$n = 2$▫, there are bijective linear maps ▫$\Phi$▫ on ▫$\mathcal{H}_n(\mathbb{F})$▫ and ▫$M_n(\mathbb{F})$▫ satisfyi... ...mathematics, linear algebra, matrix theory, permanent, determinant... Keywords: mathematics, linear algebra, matrix theory, permanent, determinant Published: 03.04.2017; Views: 655; Downloads: 48 Full text (0,00 KB) 
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