Linear maps preserving pairs of Hermitian matrices on which the rank is additive and applications
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Publication:2574340
DOI10.1007/BF02935803zbMath1083.15004OpenAlexW2034707524MaRDI QIDQ2574340
Chong Guang Cao, Xiao-ming Tang
Publication date: 21 November 2005
Published in: Journal of Applied Mathematics and Computing (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1007/bf02935803
Hermitian matrixLinear preserverSkew-Hermitian matrixAdjoint matrixJordan homomorphism.Rank-additive
Hermitian, skew-Hermitian, and related matrices (15B57) Linear transformations, semilinear transformations (15A04) Vector spaces, linear dependence, rank, lineability (15A03)
Related Items (5)
Extremal ranks of submatrices in an Hermitian solution to the matrix equation \(AXA^{*}=B\) with applications ⋮ Invertible linear maps preserving \(\{1\}\)-inverses of matrices over PID ⋮ Additive rank-1 preservers between spaces of Hermitian matrices ⋮ Additive maps on hermitian matrices ⋮ Some properties of submatrices in a solution to the matrix equations \(AX=C, XB=D\)
Cites Work
- Linear preservers on matrices
- Characterization of Jordan homomorphism on \(M_ n\) using preserving properties
- Linear operators preserving adjoint matrix between matrix spaces
- 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.
- The general Hermitian nonnegative-definite and positive-definite solutions to the matrix equation \(GXG^{\ast} + HY H^{\ast}=C\)
- Additive operators preserving rank-additivity on symmetry matrix spaces
- Linear operators that preserve pairs of matrices which satisfy extreme rank properties
- Hua's fundamental theorems of the geometry of matrices and related results
- A class of binary matrices preserving rank under matrix addition and its application
- Linear preservers on spaces of Hermitian or real symmetric matrices
- Linear preservers for matrix inequalities and partial orderings
- Modular automorphisms preserving idempotence and Jordan isomorphisms of triangular matrices over commutative rings
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