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Najdeno v: ključnih besedah
Povzetek najdenega: ...matematika, linear algebra, aditivni ohranjevalec, rang, ...
Ključne besede: matematika, linear algebra, aditivni ohranjevalec, rang
Objavljeno: 15.10.2013; Ogledov: 2705; Prenosov: 22
Polno besedilo (0,00 KB)

Opis: It is proved that a linear surjection ▫$\Phi: \mathcal{A} \to \mathcal{B}$▫, which preserves noninvertibility between semisimple, unital, complex Banach algebras, is automatically injective.
Najdeno v: ključnih besedah
Povzetek najdenega: ...It is proved that a linear surjection ▫$\Phi: \mathcal{A} \to \mathcal{B}$▫, which preserves... ...analysis, linear preserver, noninvertible element, semisimple Banach algebra, socle...
Ključne besede: mathematics, functional analysis, linear preserver, noninvertible element, semisimple Banach algebra, socle
Objavljeno: 15.10.2013; Ogledov: 2376; Prenosov: 120
Polno besedilo (0,00 KB)

Opis: 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.
Najdeno v: ključnih besedah
Povzetek najdenega: ...mathematics, linear algebra, additive preserver, hermitian matrices, rank, Galois...
Ključne besede: mathematics, linear algebra, additive preserver, hermitian matrices, rank, Galois field, weak homomorphism of a graph
Objavljeno: 03.04.2017; Ogledov: 1826; Prenosov: 76
Polno besedilo (0,00 KB)
Gradivo ima več datotek! Več...

Opis: Let ▫$M_n$▫ be the algebra of all ▫$n \times n$▫ matrices over ▫$\mathbb{C}$▫. We say that ▫$A, B \in M_n$▫ quasi-commute if there exists a nonzero ▫$\xi \in \mathbb{C}$▫ such that ▫$AB = \xi BA$▫. In the paper we classify bijective not necessarily linear maps ▫$\Phi \colon M_n \to M_n$▫ which preserve quasi-commutativity in both directions.
Najdeno v: ključnih besedah
Povzetek najdenega: ...the paper we classify bijective not necessarily linear maps ▫$\Phi \colon M_n \to M_n$▫ which... ...Let ▫$M_n$▫ be the algebra of all ▫$n \times n$▫ matrices over...
Ključne besede: mathematics, linear algebra, general preserver, matrix algebra, quasi-commutativity
Objavljeno: 03.04.2017; Ogledov: 1424; Prenosov: 75
Polno besedilo (0,00 KB)

Opis: 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.
Najdeno v: ključnih besedah
Povzetek najdenega: ...for ▫$n = 2$▫, there are bijective linear maps ▫$\Phi$▫ on ▫$\mathcal{H}_n(\mathbb{F})$▫ and ▫$M_n(\mathbb{F})$▫ satisfyi... ...mathematics, linear algebra, matrix theory, permanent, determinant...
Ključne besede: mathematics, linear algebra, matrix theory, permanent, determinant
Objavljeno: 03.04.2017; Ogledov: 1539; Prenosov: 85
Polno besedilo (0,00 KB)