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1.
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

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: 1667; Downloads: 8
URL Full text (0,00 KB)

2.
Jordan triple product homomorphisms
Bojan 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: 1656; Downloads: 67
URL Full text (0,00 KB)

3.
Noninvertibility preservers on Banach algebras
Bojan 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: 1267; Downloads: 55
URL Full text (0,00 KB)

4.
General preservers of quasi-commutativity on hermitian matrices
Bojan 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 ▫$A,B \in H_n$▫ 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: ključnih besedah
Summary of found: ...▫$AB = \xi BA$▫ Bijective not necessarily linear maps on hermitian matrices which preserve quasi-commutativity... ...mathematics, linear algebra, general preserver, hermitian matrices, quasi-commutativity...
Keywords: mathematics, linear algebra, general preserver, hermitian matrices, quasi-commutativity
Published: 03.04.2017; Views: 680; Downloads: 101
URL Full text (0,00 KB)
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5.
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.
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: 766; Downloads: 27
URL Full text (0,00 KB)
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6.
General preservers of quasi-commutativity on self-adjoint operators
Bojan 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 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: ključnih besedah
Summary of found: ...${\mathcal B}_{sa}(H)▫$ the set of all bounded linear self-adjoint operators. We say that ▫$A, B... ...mathematics, linear algebra, general preserver, self-adjoint operator, quasi-commutativity...
Keywords: mathematics, linear algebra, general preserver, self-adjoint operator, quasi-commutativity
Published: 03.04.2017; Views: 699; Downloads: 41
URL Full text (0,00 KB)

7.
General preservers of quasi-commutativity
Bojan 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 ▫$A, B \in M_n$▫ 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: 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, quasi-commutativity
Published: 03.04.2017; Views: 539; Downloads: 43
URL Full text (0,00 KB)

8.
On maximal distances in a commuting graph
Bojan 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 non-derogatory. Rank-one 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: 699; Downloads: 92
URL Full text (0,00 KB)
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9.
Permanent versus determinant over a finite field
Gregor 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: 662; Downloads: 49
URL Full text (0,00 KB)

10.
Wittov izrek
Narmina Baghirova, 2018, undergraduate thesis

Found in: ključnih besedah
Summary of found: ...Witt's theorem, linear algebra, bilinear forms...
Keywords: Witt's theorem, linear algebra, bilinear forms
Published: 17.09.2018; Views: 189; Downloads: 8
URL Full text (0,00 KB)

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