1. Rankpermutable additive mappingsAleksandr Èmilevič Guterman, Anna A. Alieva, Bojan Kuzma, 2006, original scientific article Abstract: Let ▫$\sigma$▫ be a fixed nonidentical permutation on ▫$k$▫ elements. Additive bijections ▫$T$▫ on the matrix algebra ▫$M_n(\mathbb{F})$▫ over a field ▫$\mathbb{F}$▫ of characteristic zero, with the property that ▫$\rm{rk} (A_1...A_k) = \rm{rk} (A_{\sigma(1)}...A_{\sigma(k)})$▫ implies the same condition on the ▫$T$▫ images, are characterized. It is also shown that the surjectivity assumption can be relaxed, if this property is preserved in both directions. Found in: ključnih besedah Summary of found: ...▫$k$▫ elements. Additive bijections ▫$T$▫ on the matrix algebra ▫$M_n(\mathbb{F})$▫ over a field ▫$\mathbb{F}$▫ of... Keywords: mathematics, linearna algebra, matrix algebra, rank, permutation, additive preservers Published: 15.10.2013; Views: 2632; Downloads: 85 Full text (0,00 KB) 
2. Qpolynomial distanceregular graphs with a [sub] 1 [equal] 0 and a [sub] 2 [not equal] 0Štefko Miklavič, 2008, original scientific article Abstract: Let ▫$\Gamma$▫ denote a ▫$Q$▫polynomial distanceregular graph with diameter ▫$D \ge 3$▫ and intersection numbers ▫$a_1=0$▫, ▫$a_2 \ne 0$▫. Let ▫$X$▫ denote the vertex set of ▫$\Gamma$▫ and let ▫$A \in {\mathrm{Mat}}_X ({\mathbb{C}})$▫ denote the adjacency matrix of ▫$\Gamma$▫. Fix ▫$x \in X$▫ and let denote $A^\ast \in {\mathrm{Mat}}_X ({\mathbb{C}})$ the corresponding dual adjacency matrix. Let ▫$T$▫ denote the subalgebra of ▫$A{\mathrm{Mat}}_X ({\mathbb{C}})$▫ generated by ▫$A$▫, ▫$A^\ast$▫. We call ▫$T$▫ the Terwilliger algebra of ▫$\Gamma$▫ with respect to ▫$x$▫. We show that up to isomorphism there exists a unique irreducible ▫$T$▫module ▫$W$▫ with endpoint 1. We show that ▫$W$▫ has dimension ▫$2D2$▫. We display a basis for ▫$W$▫ which consists of eigenvectors for ▫$A^\ast$▫. We display the action of ▫$A$▫ on this basis. We show that ▫$W$▫ appears in the standard module of ▫$\Gamma$▫ with multiplicity ▫$k1$▫, where ▫$k$▫ is the valency of ▫$\Gamma$▫. Found in: ključnih besedah Summary of found: ...▫$A \in {\mathrm{Mat}}_X ({\mathbb{C}})$▫ denote the adjacency matrix of ▫$\Gamma$▫. Fix ▫$x \in X$▫ and... ...dual adjacency matrix. Let ▫$T$▫ denote the sub algebra of ▫$A{\mathrm{Mat}}_X ({\mathbb{C}})$▫ generated by ▫$A$▫, ▫$A^\ast$▫.... Keywords: mathematics, graph theory, adjacency matrix, distanceregular graph, Terwilliger algebra Published: 15.10.2013; Views: 3251; Downloads: 27 Full text (0,00 KB) 
3. Jordan [tau]derivations of locally matrix ringsAjda Fošner, ChenLian Chuang, Tsiu Kwen Lee, 2013, original scientific article Abstract: Let ▫$R$▫ be a prime, locally matrix ring of characteristic not 2 and let ▫$Q_{ms}(R)$▫ be the maximal symmetric ring of quotients of ▫$R$▫. Suppose that ▫$\delta \colon R \to Q_{ms}(R)$▫ is a Jordan ▫$\tau$▫derivation, where ▫$\tau$▫ is an antiautomorphism of $R$. Then there exists ▫$a \in Q_{ms}(R)$▫ such that ▫$\delta(x) = xa  a\tau(x)$▫ for all ▫$x \in R$▫. Let ▫$X$▫ be a Banach space over the field ▫$\mathbb{F}$▫ of real or complex numbers and let ▫$\mathcal{B}(X)$▫ be the algebra of all bounded linear operators on ▫$X$▫. We prove that ▫$Q_{ms}(\mathcal{B}(X)) = \mathcal{B}(X)$▫, which provides the viewpoint of ring theory for some results concerning derivations on the algebra ▫$\mathcal{B}(X)$▫. In particular, all Jordan ▫$\tau$▫derivations of ▫$\mathcal{B}(X)$▫ are inner if ▫$\dim_{\mathbb{F}} X>1$▫. Found in: ključnih besedah Summary of found: ...complex numbers and let ▫$\mathcal{B}(X)$▫ be the algebra of all bounded linear operators on ▫$X$▫.... Keywords: mathematics, algebra, antiautomorphism, locally matrix ring, prime ring, Jordan homomorphism, Jordan ▫$\tau$▫derivation, Banach space Published: 15.10.2013; Views: 2840; Downloads: 76 Full text (0,00 KB) 
4. 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 preserver... Keywords: mathematics, linear algebra, matrix algebra, Jordan triple product, nonlinear preserver Published: 15.10.2013; Views: 3237; Downloads: 134 Full text (0,00 KB) 
5. Mappings that preserve pairs of operators with zero triple Jordan productGorazd Lešnjak, Bojan Kuzma, Mirko Dobovišek, ChiKwong Li, Tatjana Petek, 2007, original scientific article Abstract: Let ▫$\mathbb{F}$▫ be a field and ▫$n \ge 3$▫. Suppose ▫${\mathfrak{G_1,G_2}} \subseteq M_n(\mathbb{F})▫$ contain all rankone idempotents. The structure of surjections ▫$\phi : \mathfrak{G_1} \to \mathfrak{G_2}$▫ satisfying ▫$ABA = 0 \iff \phi(A)\phi(B)\phi(A) = 0$▫ is determined. Similar results are also obtained for (a) subsets of bounded operators acting on a complex or real Banach space, (b) the space of Hermitian matrices acting on ▫$n$▫dimensional vectors over a skewfield, (c) subsets of selfadjoint bounded linear operators acting on an infinite dimensional complex Hilbert space. It is then illustrated that the results can be applied to characterize mappings ▫$\phi$▫ on matrices or operators such that ▫$F(ABA) = F(\phi(A)\phi(B)\phi(A))▫$ for all ▫$A,B$▫ for functions ▫$F$▫ such as the spectral norm, Schatten ▫$p$▫norm, numerical radius and numerical range, etc. Found in: ključnih besedah Summary of found: ... matrix algebra, Jordan triple product, nonlinear preservers... Keywords: matrix algebra, Jordan triple product, nonlinear preservers Published: 03.04.2017; Views: 1830; Downloads: 93 Full text (0,00 KB) 
6. General preservers of quasicommutativityGregor Dolinar, Bojan Kuzma, 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: ...mathematics, linear algebra, general preserver, matrix algebra, quasicommutativity... Keywords: mathematics, linear algebra, general preserver, matrix algebra, quasicommutativity Published: 03.04.2017; Views: 1412; Downloads: 75 Full text (0,00 KB) 
7. On maximal distances in a commuting graphBojan Kuzma, Gregor Dolinar, 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 nonderogatory. Rankone matrices and diagonalizable matrices are also characterized in terms of the commuting graph. Found in: ključnih besedah Summary of found: ...mathematics, linear algebra, graph theory, commuting graph, matrix algebra, algebraically closed field, centralizer, distance in... 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: 1712; Downloads: 230 Full text (0,00 KB) This document has more files! More...

8. Permanent versus determinant over a finite fieldAleksandr Èmilevič Guterman, Gregor Dolinar, 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. Found in: ključnih besedah Summary of found: ...Hermitian matrices ▫$\mathcal{H}_n(\mathbb{F})$▫ and for the whole matrix space ▫$M_n(\mathbb{F})$▫. It is known that for... ...mathematics, linear algebra, matrix theory, permanent, determinant... Keywords: mathematics, linear algebra, matrix theory, permanent, determinant Published: 03.04.2017; Views: 1536; Downloads: 85 Full text (0,00 KB) 