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42. Tang, Xiao-Ming; Cao, Chong-Guang: Linear maps preserving pairs of Hermitian matrices on which the rank is additive and applications. (English). - [J] J. Appl. Math. Comput. 19, No. 1-2, 253-260 (2005). [ISSN 1598-5865]Bojan Kuzma, 2006, recenzija, prikaz knjige, kritika Ključne besede: matematika, linearna algebra, ohranjevalci, hermitska matrika, adjungirana matrika, jordanski homomorfizem Objavljeno v RUP: 15.10.2013; Ogledov: 2214; Prenosov: 34 Povezava na celotno besedilo |
43. Lim, M.H.: Additive mappings between Hermitian matrix spaces preserving rank not exceeding one. (English). - [J] Linear Algebra Appl. 408, 259-267 (2005). [ISSN 0024-3795]Bojan Kuzma, 2006, recenzija, prikaz knjige, kritika Ključne besede: matematika, linearna algebra, aditivna preslikava, hermitska matrika, ohranjevalec, rang Objavljeno v RUP: 15.10.2013; Ogledov: 2548; Prenosov: 32 Povezava na celotno besedilo |
44. Hyers-Ulam-Rassias stability of generalized module left (m,n)-derivationsAjda Fošner, 2013, izvirni znanstveni članek Opis: The generalized Hyers-Ulam-Rassias stability of generalized module left ▫$(m,n)$▫-derivations on a normed algebra ▫$\mathcal{A}$▫ into a Banach left ▫$\mathcal{A}$▫-module is established. Ključne besede: Hyers-Ulam-Rassias stability, normed algebra, Banach left A-module, module left (m, n)-derivation, generalized module left (m, n)-derivation Objavljeno v RUP: 15.10.2013; Ogledov: 3464; Prenosov: 107 Povezava na celotno besedilo |
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46. Ob otobraženijah, sohranjajuščih immanantyBojan Kuzma, 2007, izvirni znanstveni članek Opis: V članku študiramo preslikave, ki transformirajo eno imananto matričnih snopov v drugo. Vnaprej ne predpostavimo niti surjektivnosti, niti linearnosti preslikav. Predpostavimo zgolj šibko linearnost v obliki identitete ▫$d_chi (Phi(A) + lambda Phi(B)) = d_{chi'}(A+lambda B)$▫. Pokažemo, da zgolj ta identiteta implicira avtomatično linearnost in bijektivnost preslikave ▫$Phi$▫. Ključne besede: matematika, linearna algebra, teorija matrik, imanante, ohranjevalci Objavljeno v RUP: 15.10.2013; Ogledov: 2879; Prenosov: 90 Povezava na celotno besedilo |
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48. 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, recenzija, prikaz knjige, kritika Ključne besede: matematika, linear algebra, aditivni ohranjevalec, rang Objavljeno v RUP: 15.10.2013; Ogledov: 3511; Prenosov: 25 Povezava na celotno besedilo |
49. On bipartite Q-polynominal distance-regular graphsŠtefko Miklavič, 2007, izvirni znanstveni članek Opis: Let ▫$\Gamma$▫ denote a bipartite ▫$Q$▫-polynomial distance-regular graph with vertex set ▫$X$▫, diameter ▫$d \ge 3$▫ and valency ▫$k \ge 3$▫. Let ▫${\mathbb{R}}^X$▫ denote the vector space over ▫$\mathbb{R}$▫ consisting of column vectors with entries in ▫$\mathbb{r}$▫ and rows indexed by ▫$X$▫. For ▫$z \in X$▫, let ▫$\hat{z}$▫ denote the vector in ▫${\mathbb{R}}^X$▫ with a 1 in the ▫$z$▫-coordinate, and 0 in all other coordinates. Fix ▫$x,y \in X$▫ such that ▫$\partial(x,y)=2▫, where ▫$\partial$▫ denotes the path-length distance. For ▫$0 \le i,j \le d$▫ define ▫$w_{ij} = \sum\hat{z}$▫, where the sum is over all ▫$z \in X$▫ such that ▫$\partial(x,z) = i$▫ and ▫$\partial(y,z) = j▫$. We define ▫$W = \textrm{span} \{w_{ij}|0 \le i,j \le d\}$▫. In this paper we consider the space ▫$MW = \textrm{span} \{mw |m \in M, w \in W \l\}$▫, where ▫$M$▫ is the Bose-Mesner algebra of ▫$\Gamma$▫. We observe that ▫$MW$▫ is the minimal ▫$A$▫-invariant subspace of ▫${\mathbb{R}}^X$▫ which contains ▫$W$▫, where ▫$A$▫ is the adjacency matrix of ▫$\Gamma$▫. We display a basis for ▫$MW$▫ that is orthogonal with respect to the dot product. We give the action of ▫$A$▫ on this basis. We show that the dimension of ▫$MW$▫ is ▫$3d-3$▫ if ▫$\Gamma$▫ is 2-homogeneous, ▫$3d-1$▫ if ▫$\Gamma$▫ is the antipodal quotient of the ▫$2d$▫-cube, and ▫$4d-4$▫ otherwise. We obtain our main result using Terwilliger's "balanced set" characterization of the ▫$Q$▫-polynomial property. Ključne besede: mathematics, graph theory, distance-regular graphs, ▫$Q$▫-polynominal property, Bose-Mesner algebra, balanced set characterization of the Q-polynominal property Objavljeno v RUP: 15.10.2013; Ogledov: 3659; Prenosov: 28 Povezava na celotno besedilo |
50. Alieva, Anna A.; Guterman, Alexander E.: Monotone linear transformations on matrices are invertible. (English). - [J] Commun. Algebra 33, No. 9, 3335-3352 (2005). [ISSN 0092-7872; ISSN 1532-4125]Bojan Kuzma, 2006, recenzija, prikaz knjige, kritika Ključne besede: matematika, linearna algebra, linearni ohranjevalci, matrične delne urejenosti, monotona transformacija Objavljeno v RUP: 15.10.2013; Ogledov: 2733; Prenosov: 42 Povezava na celotno besedilo |