71. Permanent versus determinant over a finite fieldGregor Dolinar, Aleksandr Èmilevič Guterman, 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.
Keywords: mathematics, linear algebra, matrix theory, permanent, determinant
Published in RUP: 03.04.2017; Views: 2096; Downloads: 125
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72. Maps on self-adjoint operators preserving numerical range of products up to a factorKan He, Jin Chuan Hou, Gregor Dolinar, Bojan Kuzma, 2011, original scientific article Abstract: Let ▫$H$▫ be a complex Hilbert space and ▫${mathscr{S}}_a(H)$▫ the space of all self adjoint operators on ▫$H$▫. ▫$Phi colon {mathscr{S}}_a(H) to {mathscr{S}}_a(H)$▫ is a surjective map. For ▫$xi, eta in mathbb{C} setminus {1}$▫, then ▫$Phi$▫ satisfies that ▫$$W(AB - xi BA) = W(Phi(A)Phi(B) - etaPhi(B)phi(A))$$▫ for all ▫$A,B in {mathscr{S}}_a(H)$▫ if and only if there exists a unitary operator or con-unitary operator ▫$U$▫ such that ▫$Phi(A) = UAU^ast$▫ for all ▫$A in {mathscr{S}}_a(H)$▫ or ▫$Phi(A) = -UAU^ast$▫ for all ▫$A in {mathscr{S}}_a(H)$▫.
Keywords: matematika, teorija operatorjev, numerični zaklad, ohranjevalci
Published in RUP: 03.04.2017; Views: 2320; Downloads: 32
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78. Variations of phenolic compounds and sensory properties of virgin olive oils from the variety 'Istrska belica'Milena Bučar-Miklavčič, Terezija Golob, Vasilij Valenčič, Erika Bešter, Bojan Butinar, Ana Miklavčič Višnjevec, 2016, original scientific article Keywords: olive oil, phenolic compounds, sensory properties, Istrska belica
Published in RUP: 08.08.2016; Views: 3240; Downloads: 123
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79. Age and growth dynamics of spiny dogfish, Squalus acanthias, in the Adriatic Sea (Eastern Mediterranean Sea)Romana Gračan, Scott A. Heppell, Gordana Lacković, Bojan Lazar, 2014, published scientific conference contribution abstract Keywords: spiny dogfish, Squalus acanthias, Adriatic Sea, age
Published in RUP: 08.08.2016; Views: 2621; Downloads: 91
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