Maps on spaces of symmetric matrices preserving idempotence

DOI10.1016/j.laa.2006.08.012zbMath1111.15003OpenAlexW2032364921MaRDI QIDQ861024

Yu Qiu Sheng, Baodong Zheng, Xian Zhang

Publication date: 9 January 2007

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

Full work available at URL: https://doi.org/10.1016/j.laa.2006.08.012

zbMATH Keywords

Symmetric matrixFieldIdempotence preserver

Mathematics Subject Classification ID

Hermitian, skew-Hermitian, and related matrices (15B57) Linear transformations, semilinear transformations (15A04)

Related Items

Maps on \({\mathcal B}({\mathcal H})\) preserving involution ⋮ Maps preserving idempotence on matrix spaces ⋮ Idempotence preserving maps between matrix spaces

Cites Work

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• Maps on matrix algebras preserving idempotents
• Linear operators that preserve pairs of matrices which satisfy extreme rank properties -- a supplementary version.
• Idempotence-preserving maps without the linearity and surjectivity assumptions
• Linear preservers between matrix modules over connected commutative rings
• Hua's fundamental theorems of the geometry of matrices and related results
• Order preserving maps on the poset of upper triangular idempotent matrices
• Linear Preserver Problems
• Automorphisms of the poset of upper triangular idempotent matrices

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