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1.
Adjacency preservers, symmetric matrices, and cores
Marko Orel, 2012, original scientific article

Abstract: 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: osebi
Keywords: adjacency preserver, symmetric matrix, finite field, eigenvalue of a graph, coloring, quadratic form
Published: 15.10.2013; Views: 1404; Downloads: 64
URL Full text (0,00 KB)

2.
Additive mappings on symmetric matrices
Bojan Kuzma, Marko Orel, 2006, original scientific article

Abstract: Klasificirane so aditivne preslikave, ki ne povečujejo minimalnega ranga na simetričnih matrikah s koeficienti iz komutativnega obsega karakteristike dve ali tri.
Found in: osebi
Keywords: matematika, linearna algebra, aditivni ohranjevalci, simetrična matrika, rang
Published: 15.10.2013; Views: 1056; Downloads: 41
URL Full text (0,00 KB)

3.
Adjacency preservers on symmetric matrices over a finite field
Marko Orel, 2011, published scientific conference contribution abstract

Found in: osebi
Keywords: matematika, linearna algebra, ohranjevalci sosednosti, simetrične matrike
Published: 15.10.2013; Views: 1365; Downloads: 22
URL Full text (0,00 KB)
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4.
Kvadratne forme nad končnimi obsegi
Borut Umer, 2014, undergraduate thesis

Found in: osebi
Keywords: končni obseg, polja, sled elementa, kvadratna forma
Published: 10.07.2015; Views: 844; Downloads: 8
URL Full text (0,00 KB)

5.
Zbirka rešenih izpitov in kolokvijev iz statistike za biopsihologe
Marko Orel, 2015, other educational material

Found in: osebi
Keywords: osnovni statistični pojmi, univariantna analiza, bivariantna analiza
Published: 15.10.2015; Views: 798; Downloads: 24
URL Full text (0,00 KB)
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6.
Nekaj malega o modeliranju, matrikah in metodi najmanjših kvadratov
Marko Orel, 2015, other educational material

Found in: osebi
Keywords: matrike, vektorji, metoda najmanjših kvadratov, prilagajanje krivulj
Published: 15.10.2015; Views: 906; Downloads: 71
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7.
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Additive rank-one nonincreasing maps on Hermitian matrices over the field GF(2[sup]2)
Marko Orel, Bojan Kuzma, 2009, original scientific article

Abstract: 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: osebi
Keywords: mathematics, linear algebra, additive preserver, hermitian matrices, rank, Galois field, weak homomorphism of a graph
Published: 03.04.2017; Views: 740; Downloads: 26
URL Full text (0,00 KB)
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9.
Permanent versus determinant over a finite field
Gregor Dolinar, Aleksandr Èmilevič Guterman, Marko Orel, Bojan Kuzma, 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: osebi
Keywords: mathematics, linear algebra, matrix theory, permanent, determinant
Published: 03.04.2017; Views: 643; Downloads: 48
URL Full text (0,00 KB)

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