11. Additive rank-one nonincreasing maps on Hermitian matrices over the field GF(2[sup]2)Marko Orel, Bojan Kuzma, 2009, izvirni znanstveni članek Opis: 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.
Ključne besede: mathematics, linear algebra, additive preserver, hermitian matrices, rank, Galois field, weak homomorphism of a graph
Objavljeno v RUP: 03.04.2017; Ogledov: 2536; Prenosov: 87
 Povezava na celotno besedilo |
12. |
13. |
14. On maximal distances in a commuting graphGregor Dolinar, Bojan Kuzma, Polona Oblak, 2012, izvirni znanstveni članek Opis: 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.
Ključne besede: 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
Objavljeno v RUP: 03.04.2017; Ogledov: 2318; Prenosov: 256
Povezava na celotno besedilo |
15. Permanent versus determinant over a finite fieldGregor Dolinar, Aleksandr Èmilevič Guterman, Bojan Kuzma, Marko Orel, 2013, objavljeni znanstveni prispevek na konferenci Opis: 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.
Ključne besede: mathematics, linear algebra, matrix theory, permanent, determinant
Objavljeno v RUP: 03.04.2017; Ogledov: 2128; Prenosov: 125
Povezava na celotno besedilo |
16. Maps on self-adjoint operators preserving numerical range of products up to a factorKan He, Jin Chuan Hou, Gregor Dolinar, Bojan Kuzma, 2011, izvirni znanstveni članek Opis: 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 ▫$A in {mathscr{S}}_a(H)$▫.
Ključne besede: matematika, teorija operatorjev, numerični zaklad, ohranjevalci
Objavljeno v RUP: 03.04.2017; Ogledov: 2347; Prenosov: 32
Povezava na celotno besedilo |
17. |
18. |
19. |
20. |
