SCHUR MULTIPLICATIVE MAPS ON MATRICES
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Publication:5387226
DOI10.1017/S0004972708000051zbMath1147.15001MaRDI QIDQ5387226
Chi-Kwong Li, Ashwin Rastogi, Sean Clark
Publication date: 8 May 2008
Published in: Bulletin of the Australian Mathematical Society (Search for Journal in Brave)
eigenvaluesinvertible matricesHadamard productsingular matricesrankdeterminantSchur productrank-\(k\) matriceslinear maps preserving the determinant functionslinear maps preserving the set of singular matricesSchur multiplicative map
Theory of matrix inversion and generalized inverses (15A09) Determinants, permanents, traces, other special matrix functions (15A15) Linear transformations, semilinear transformations (15A04) Vector spaces, linear dependence, rank, lineability (15A03)
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Unitary similarity invariant function preservers of skew products of operators ⋮ The Schur multiplicative and harmonic convexities of the complete symmetric function ⋮ Schur-multiplicative maps preserving unitarily invariant norms
Cites Work
- Maps on matrix spaces
- Multiplicative maps on matrices that preserve the spectrum
- On determinant preserver problems
- Determinant preserving maps on matrix algebras
- Multiplicative preservers on semigroups of matrices
- Multiplicative maps of matrix semi-groups
- Linear Preserver Problems
- Linear Transformations on Algebras of Matrices: The Invariance of the Elementary Symmetric Functions
- Linear transformations of the second elementary function
- Linear Transformations on Matrices: the Invariance of the Third Elementary Symmetric Function
- Linear operators on matrices: The invariance of rank-k matrices
