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 1 - 10 / 2012 1.Adjacency preservers, symmetric matrices, and coresMarko Orel, 2012, original scientific articleAbstract: It is shown that the graph ▫$\Gamma_n$▫ that has the set of all ▫$n \times n$▫ symmetric matrices over a finite field as the vertex set, with two matrices being adjacent if and only if the rank of their difference equals one, is a core if ▫$n \ge 3$▫. Eigenvalues of the graph ▫$\Gamma_n$▫ are calculated as well.Found in: osebiKeywords: adjacency preserver, symmetric matrix, finite field, eigenvalue of a graph, coloring, quadratic formPublished: 15.10.2013; Views: 1625; Downloads: 85 Full text (0,00 KB) 2.Additive mappings on symmetric matricesBojan Kuzma, Marko Orel, 2006, original scientific articleAbstract: Klasificirane so aditivne preslikave, ki ne povečujejo minimalnega ranga na simetričnih matrikah s koeficienti iz komutativnega obsega karakteristike dve ali tri.Found in: osebiKeywords: matematika, linearna algebra, aditivni ohranjevalci, simetrična matrika, rangPublished: 15.10.2013; Views: 1285; Downloads: 53 Full text (0,00 KB) 3.Adjacency preservers on symmetric matrices over a finite fieldMarko Orel, 2011, published scientific conference contribution abstractFound in: osebiKeywords: matematika, linearna algebra, ohranjevalci sosednosti, simetrične matrikePublished: 15.10.2013; Views: 1590; Downloads: 25 Full text (0,00 KB)This document has more files! More... 4.Kvadratne forme nad končnimi obsegiBorut Umer, 2014, undergraduate thesisFound in: osebiKeywords: končni obseg, polja, sled elementa, kvadratna formaPublished: 10.07.2015; Views: 989; Downloads: 8 Full text (0,00 KB) 5.Zbirka rešenih izpitov in kolokvijev iz statistike za biopsihologeMarko Orel, 2015, other educational materialFound in: osebiKeywords: osnovni statistični pojmi, univariantna analiza, bivariantna analizaPublished: 15.10.2015; Views: 953; Downloads: 28 Full text (0,00 KB)This document has more files! More... 6.Nekaj malega o modeliranju, matrikah in metodi najmanjših kvadratovMarko Orel, 2015, other educational materialFound in: osebiKeywords: matrike, vektorji, metoda najmanjših kvadratov, prilagajanje krivuljPublished: 15.10.2015; Views: 1123; Downloads: 75 Full text (0,00 KB)This document has more files! More... 7.Verjetnost za nematematike. Pregled teorije in izbrane rešene nalogeMarko Orel, 2015, other educational materialFound in: osebiKeywords: elementarna verjetnost, diskretne slučajne spremenljivke, zvezne slučajne spremenljivke, porazdelitvena funkcija, kvantili, večrazsežna porazdelitev, robna porazdelitev, pričakovana vrednost, varianca, centralni limitni izrekPublished: 15.10.2015; Views: 1232; Downloads: 65 Full text (0,00 KB)This document has more files! More... 8.Additive rank-one nonincreasing maps on Hermitian matrices over the field GF(2[sup]2)Marko Orel, Bojan Kuzma, 2009, original scientific articleAbstract: 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: osebiKeywords: mathematics, linear algebra, additive preserver, hermitian matrices, rank, Galois field, weak homomorphism of a graphPublished: 03.04.2017; Views: 983; Downloads: 31 Full text (0,00 KB)This document has more files! More... 9.Permanent versus determinant over a finite fieldGregor Dolinar, Aleksandr Èmilevič Guterman, Marko Orel, Bojan Kuzma, 2013, published scientific conference contributionAbstract: 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: osebiKeywords: mathematics, linear algebra, matrix theory, permanent, determinantPublished: 03.04.2017; Views: 811; Downloads: 66 Full text (0,00 KB) 10.On generalizations of the Petersen graph and the Coxeter graphMarko Orel, 2015, original scientific articleFound in: osebiKeywords: Petersenov graf, Coexerjev graf, hermitske matrike, simetrične matrike, Coexter graph, Petersen graph, Hermitian matrix, symmetric matrixPublished: 03.04.2017; Views: 837; Downloads: 40 Full text (0,00 KB)
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