Additive preservers of rank-additivity on the spaces of symmetric and alternate matrices.
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Publication:1428620
DOI10.1016/j.laa.2003.10.008zbMath1059.15009OpenAlexW2065595610MaRDI QIDQ1428620
Publication date: 29 March 2004
Published in: Linear Algebra and its Applications (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1016/j.laa.2003.10.008
automorphismssymmetric matrixlinear transformationspreserversnon-associative algebrasalternate matrixrank additivity
Linear transformations, semilinear transformations (15A04) Vector spaces, linear dependence, rank, lineability (15A03)
Related Items (13)
Linear/additive preservers of ranks 2 and 4 on alternate matrix spaces over fields ⋮ Additive mappings on symmetric matrices ⋮ Additive mappings that do not increase minimal rank of alternate matrices ⋮ Geometry of Alternate Matrices over Bezout Domains ⋮ Additive rank-1 preservers between Hermitian matrix spaces and applications ⋮ Additive maps on hermitian matrices ⋮ Additive preservers of rank-additivity on matrix spaces ⋮ Additive preservers of rank on alternate matrix spaces over fields and applications ⋮ Additive rank-one preservers on block triangular matrix spaces ⋮ Linear preservers of rank-sum-maximum, rank, rank-subtractivity, and rank-sum-minimum on symmetric matrices ⋮ Additive adjoint preservers between matrix spaces ⋮ Diameter preserving surjection on alternate matrices ⋮ Linear maps preserving pairs of Hermitian matrices on which the rank is additive and applications
Cites Work
- Linear preserver problems: A brief introduction and some special techniques
- Linear operators that preserve pairs of matrices which satisfy extreme rank properties
- Linear transformations between matrix spaces that map one rank specific set into another
- Linear preservers for matrix inequalities and partial orderings
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