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3. Additive rank-one 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 rank-one 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 rank-additivity preserving maps, are extended to arbitrary fields. An application concerning the preservers of hermitian varieties is also presented. Keywords: mathematics, linear algebra, additive preserver, hermitian matrices, rank, Galois field, weak homomorphism of a graph Published in RUP: 03.04.2017; Views: 2552; Downloads: 87 Link to full text |
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6. On maximal distances in a commuting graphGregor Dolinar, Bojan Kuzma, Polona Oblak, 2012, original scientific article Abstract: 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. 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 in RUP: 03.04.2017; Views: 2327; Downloads: 256 Link to full text |
7. Permanent versus determinant over a finite fieldGregor Dolinar, Aleksandr Èmilevič Guterman, Bojan Kuzma, Marko Orel, 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. Keywords: mathematics, linear algebra, matrix theory, permanent, determinant Published in RUP: 03.04.2017; Views: 2143; Downloads: 126 Link to full text |
8. 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. Keywords: mathematics, functional analysis, linear preserver, noninvertible element, semisimple Banach algebra, socle Published in RUP: 15.10.2013; Views: 3219; Downloads: 126 Link to full text |
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10. Cao, Chongguang; Huang, Liping; Tang, Xiaomin: Additive map preserving rank 2 on alternate matrices. (English). - [J] Afr. Diaspora J. Math 3, No. 2, 107-113 (2005). [ISSN 1539-845X]Bojan Kuzma, 2006, review, book review, critique Keywords: matematika, linear algebra, aditivni ohranjevalec, rang Published in RUP: 15.10.2013; Views: 3532; Downloads: 25 Link to full text |