Additive preservers of rank-additivity on matrix spaces

DOI10.1016/j.laa.2005.01.020zbMath1084.15006OpenAlexW2127718681MaRDI QIDQ556899

Wai-Leong Chooi, Ming-Huat Lim

Publication date: 23 June 2005

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

Full work available at URL: https://doi.org/10.1016/j.laa.2005.01.020

zbMATH Keywords

Symmetric spacesAdditive preserversRank-additivityTensor spaces

Mathematics Subject Classification ID

Linear transformations, semilinear transformations (15A04) Multilinear algebra, tensor calculus (15A69) Vector spaces, linear dependence, rank, lineability (15A03)

Related Items

A note on additive mappings decreasing rank one, On additive transformations preserving a multiplicative matrix function, Additive mappings on symmetric matrices, Monotone maps on matrices of index one, Additive preservers of non-zero decomposable tensors, Monotone additive matrix transformations, Additive rank-one preservers on block triangular matrix spaces, Additive mappings between Hermitian matrix spaces preserving rank not exceeding one

Cites Work

• Rank-one nonincreasing additive mappings on second symmetric product spaces
• The rank of a difference of matrices and associated generalized inverses
• Linear operators that preserve pairs of matrices which satisfy extreme rank properties -- a supplementary version.
• Additive preservers of rank-additivity on the spaces of symmetric and alternate matrices.
• Additive rank-one preserving mappings on triangular matrix algebras
• Some general techniques on linear preserver problems
• Additive mappings decreasing rank one
• 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
• Mappings which Preserve Idempotents, Local Automorphisms, and Local Derivations
• Linear preservers for matrix inequalities and partial orderings
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