Additive rank-one preserving surjections on symmetric matrix spaces

DOI10.1016/S0024-3795(02)00494-9zbMath1035.15005MaRDI QIDQ1863576

Xian Zhang, Chong Guang Cao

Publication date: 11 March 2003

Published in: Linear Algebra and its Applications (Search for Journal in Brave)

zbMATH Keywords

symmetric matrixfieldadditive surjectionscharacteristic polynomial preservesdeterminant preservesinvertibility preservers

Mathematics Subject Classification ID

Algebraic systems of matrices (15A30) Linear transformations, semilinear transformations (15A04) Vector spaces, linear dependence, rank, lineability (15A03)

Related Items

A note on additive mappings decreasing rank one, Additive mappings on symmetric matrices, Additive Maps Preserving Moore–Penrose Inverses of Matrices on Symmetric Matrix Spaces, Additive rank-one preservers between spaces of rectangular matrices, Jordan isomorphisms and additive rank preserving maps on symmetric matrices over PID, Permanent Polya problem for additive surjective maps, Surjective Additive Rank-1 Preservers on Hessenberg Matrices, Additive preservers of non-zero decomposable tensors, Nonstandard rank-one nonincreasing maps on symmetric matrices, Linear/additive preservers of rank 2 on spaces of alternate matrices over fields, Additive rank-1 preservers between Hermitian matrix spaces and applications, Additive maps on hermitian matrices, Rank-one nonincreasing additive mappings on second symmetric product spaces, Rank one preserving \(\mathbb R\)-linear maps on spaces of self-adjoint operators on complex Hilbert spaces, Maps preserving square-zero matrices on the algebra consisting of all upper triangular matrices, Linear maps preserving the Lorentz-cone spectrum in certain subspaces of \(M_n\), Linear preservers of rank-sum-maximum, rank, rank-subtractivity, and rank-sum-minimum on symmetric matrices, Additive mappings between Hermitian matrix spaces preserving rank not exceeding one, DETERMINANT AND SPECTRUM PRESERVING MAPS ON M_n

Cites Work

• Spectrum-preserving additive maps
• Linear preserver problems: A brief introduction and some special techniques
• Additive rank-one preserving mappings on triangular matrix algebras
• Some general techniques on linear preserver problems
• Additive mappings preserving operators of rank one
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• Additive maps preserving M-P inverses of matrices over Fields^∗
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