61. Leonard triples and hypercubesŠtefko Miklavič, 2007, izvirni znanstveni članek Opis: Let ▫$V$▫ denote a vector space over ▫$\mathbb{C}$▫ with finite positive dimension. By a Leonard triple on ▫$V$▫ we mean an ordered triple of linear operators on ▫$V$▫ such that for each of these operators there exists a basis of ▫$V$▫ with respect to which the matrix representing that operator is diagonal and the matrices representing the other two operators are irreducible tridiagonal. Let ▫$D$▫ denote a positive integer and let ▫${\mathcal{Q}}_D$▫ denote the graph of the ▫$D$▫-dimensional hypercube. Let ▫$X$ denote the vertex set of ▫${\mathcal{Q}}_D$▫ and let ▫$A \in {\mathrm{Mat}}_X ({\mathbb{C}})$▫ denote the adjacency matrix of ▫${\mathcal{Q}}_D$▫. Fix ▫$x \in X$▫ and let ▫$A^\ast \in {\mathrm{Mat}}_X({\mathbb{C}})$▫ denote the corresponding dual adjacency matrix. Let ▫$T$▫ denote the subalgebra of ▫${\mathrm{Mat}}_X({\mathbb{C}})$ generated by ▫$A,A^\ast$▫. We refer to ▫$T$▫ as the Terwilliger algebra of ▫${\mathcal{Q}}_D$▫ with respect to ▫$x$▫. The matrices ▫$A$▫ and ▫$A^\ast$▫ are related by the fact that ▫$2iA = A^\ast A^\varepsilon - A^\varepsilon A^\ast$▫ and ▫$2iA^\ast = A^\varepsilon A - AA^\varepsilon$▫, where ▫$2iA^\varepsilon = AA^\ast - A^\ast A$▫ and ▫$i^2 = -1$▫. We show that the triple ▫$A$▫, ▫$A^\ast$▫, ▫$A^\varepsilon$▫ acts on each irreducible ▫$T$▫-module as a Leonard triple. We give a detailed description of these Leonard triples. Ključne besede: mathematics, graph theory, Leonard triple, distance-regular graph, hypercube, Terwilliger algebra Objavljeno v RUP: 15.10.2013; Ogledov: 4019; Prenosov: 121 Povezava na celotno besedilo |
62. ICT adoption policy of Australian and Croatian SMEsHazbo Skoko, Branka Krivokapić-Skoko, Marinko Škare, Arnela Cerić, 2006, izvirni znanstveni članek Ključne besede: SMEs, ICT, adoption models, case studies, qualitative comparative analysis, Boolean algebra Objavljeno v RUP: 15.10.2013; Ogledov: 2682; Prenosov: 74 Povezava na celotno besedilo |
63. Q-polynomial distance-regular graphs with a [sub] 1 [equal] 0 and a [sub] 2 [not equal] 0Štefko Miklavič, 2008, izvirni znanstveni članek Opis: Let ▫$\Gamma$▫ denote a ▫$Q$▫-polynomial distance-regular 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 ▫$2D-2$▫. 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 ▫$k-1$▫, where ▫$k$▫ is the valency of ▫$\Gamma$▫. Ključne besede: mathematics, graph theory, adjacency matrix, distance-regular graph, Terwilliger algebra Objavljeno v RUP: 15.10.2013; Ogledov: 4447; Prenosov: 31 Povezava na celotno besedilo |
64. Tang, Xiao-Min; Yang, Ya-Qin: Strong linear preservers of rank reverse permutability on triangular matrices. (English). - [J] Linear Algebra Appl. 414, No. 1, 84-96 (2006). [ISSN 0024-3795]Bojan Kuzma, 2006, recenzija, prikaz knjige, kritika Ključne besede: matematika, linearna algebra, matrične algebre, linearni ohranjevalci, trikotne matrike Objavljeno v RUP: 15.10.2013; Ogledov: 3073; Prenosov: 40 Povezava na celotno besedilo |
65. Tracial numerical ranges and linear dependence of operatorsBojan Kuzma, Chi-Kwong Li, Leiba Rodman, 2011, izvirni znanstveni članek Opis: Pokazano je, da lahko linearno odvisnost dveh operatorjev na Hilbertovem prostoru preverimo s pomočjo identičnosti v modulu dane sesquilinearne oz. kvadratične forme, pridružene operatorjema. Forme so bazirane na posplošenih numeričnih zakladih. Ključne besede: matematika, linearna algebra, teorija operatorjev, Hilbertov prostor, linearni operatorji, linearna odvisnost, posplošen numerični zaklad Objavljeno v RUP: 15.10.2013; Ogledov: 3835; Prenosov: 230 Povezava na celotno besedilo |
66. Identities with generalized skew derivations on Lie idealsVincenzo De Filippis, Ajda Fošner, Feng Wei, 2013, izvirni znanstveni članek Opis: Let ▫$m, n$▫ be two nonzero fixed positive integers, ▫$R$▫ a 2-torsion free prime ring with the right Martindale quotient ring ▫$Q$▫, ▫$L$▫ a non-central Lie ideal of ▫$R$▫, and ▫$\delta$▫ a derivation of ▫$R$▫. Suppose that ▫$\alpha$▫ is an automorphism of ▫$R$▫, ▫$D$▫ a skew derivation of ▫$R$▫ with the associated automorphism ▫$\alpha$▫, and ▫$F$▫ a generalized skew derivation of ▫$R$▫ with the associated skew derivation ▫$D$▫. If ▫$$F(x^{m+n}) = F(x^m)x^n + x^m \delta (x^n)$$▫ is a polynomial identity for ▫$L$▫, then either ▫$R$▫ satisfies the standard polynomial identity ▫$s_4(x_1, x_2, x_3, x_4)$▫ of degree 4, or ▫$F$▫ is a generalized derivation of ▫$R$▫ and ▫$\delta = D$▫. Furthermore, in the latter case one of the following statements holds: (1) ▫$D = \delta = 0$▫ and there exists ▫$a \in Q$▫ such that ▫$F(x) = ax$▫ for all ▫$x \in R$▫; (2) ▫$\alpha$▫ is the identical mapping of ▫$R$▫. Ključne besede: mathematics, algebra, polynomial identity, generalized skew derivation, prime ring Objavljeno v RUP: 15.10.2013; Ogledov: 4181; Prenosov: 144 Povezava na celotno besedilo |
67. Zhang, Xian: Inverse-preserving linear maps between spaces of matrices over fields. (English). - [J] Acta Math. Sin., Engl. Ser. 22, No. 3, 873-878 (2006). [ISSN 1439-8516; ISSN 1439-7617]Bojan Kuzma, 2006, recenzija, prikaz knjige, kritika Ključne besede: matematika, linearna algebra, linearne transformacije, linearni ohranjevalci, prostori matrik Objavljeno v RUP: 15.10.2013; Ogledov: 2979; Prenosov: 27 Povezava na celotno besedilo |
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69. You, Hong; Liu, Shaowu: Linear operators preserving symplectic group over a field consisting of at least four elements. (English). - [J] Northeast. Math. J. 22, No. 2, 219-232 (2006). [ISSN 1000-1778]Bojan Kuzma, 2006, recenzija, prikaz knjige, kritika Ključne besede: matematika, linearna algebra, linearne transformacije, linearni ohranjevalci Objavljeno v RUP: 15.10.2013; Ogledov: 2732; Prenosov: 32 Povezava na celotno besedilo |
70. Norm preservers of Jordan productsBojan Kuzma, Gorazd Lešnjak, Chi-Kwong Li, Tatjana Petek, Leiba Rodman, 2011, izvirni znanstveni članek Opis: V članku klasificiramo surjektivne preslikave, ki na algebri kompleksnih matrik ohranjajo Frobeniusovo normo Jordanskega produkta. Izkaže se, da so do unitarne podobnosti in množenja s skalarnim večkratnikom vse tovrstne preslikave le štirih možnih tipov: (i) preslikava, ki je lokalno adjungiranje na normalnih matrikah in identiteta izven normalnih matrik, (ii) transponiranje, (iii) kompleksna konjugacija in (iv) adjungiranje. Do podobnih zaključkov pridemo tudi v primeru nekaterih drugih unitarno invariantnih norm, kjer pokažemo, da preslikava bodisi normalne matrike množi s skalarji, bodisi jih adjungira in množi s skalarji. Ključne besede: matematika, linearna algebra, jordanski produkt, matrična norma, ohranjevalci Objavljeno v RUP: 15.10.2013; Ogledov: 3281; Prenosov: 228 Povezava na celotno besedilo |