1. Rank-permutable additive mappingsAleksandr Èmilevič Guterman, Anna A. Alieva, Bojan Kuzma, 2006, original scientific article Abstract: Let ▫$\sigma$▫ be a fixed non-identical permutation on ▫$k$▫ elements. Additive bijections ▫$T$▫ on the matrix algebra ▫$M_n(\mathbb{F})$▫ over a field ▫$\mathbb{F}$▫ of characteristic zero, with the property that ▫$\rm{rk} (A_1...A_k) = \rm{rk} (A_{\sigma(1)}...A_{\sigma(k)})$▫ implies the same condition on the ▫$T$▫ images, are characterized. It is also shown that the surjectivity assumption can be relaxed, if this property is preserved in both directions.
Found in: ključnih besedah
Keywords: mathematics, linearna algebra, matrix algebra, rank, permutation, additive preservers
Published: 15.10.2013; Views: 2631; Downloads: 85
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2. Zhang, Xian; Sze, Nung-Sing: Additive rank-one preservers between spaces of rectangular matrices. (English). - [J] Linear Multilinear Algebra 53, No. 6, 417-425 (2005). [ISSN 0308-1087; ISSN 1563-5139]Bojan Kuzma, 2006, review, book review, critique Found in: ključnih besedah
Keywords: matematika, linearna algebra, prostor matrik, rank 1, aditivni ohranjevalec
Published: 15.10.2013; Views: 2741; Downloads: 39
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3. 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: ključnih besedah
Keywords: mathematics, linear algebra, additive preserver, hermitian matrices, rank, Galois field, weak homomorphism of a graph
Published: 03.04.2017; Views: 1822; Downloads: 75
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