Linear transformations on self-adjoint matrices: The preservation of rank-one-plus-scalar

DOI10.1016/0024-3795(86)90116-3zbMath0589.15002OpenAlexW1995795482MaRDI QIDQ1073865

William C. Waterhouse

Publication date: 1986

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

Full work available at URL: https://doi.org/10.1016/0024-3795(86)90116-3

zbMATH Keywords

linear transformationrankpreservationspace of self-adjoint linear maps

Mathematics Subject Classification ID

Commutativity of matrices (15A27) Hermitian, skew-Hermitian, and related matrices (15B57) Linear transformations, semilinear transformations (15A04)

Related Items

Chapter 2:rank and tensor rank, Chapter 4:algebraic sets, polynomials, and other functions, Linear transformations preserving symmetric rank one matrices

Cites Work

• Maps on simple algebras preserving zero products. II: Lie algebras of linear type
• Commutativity-preserving operators on symmetric matrices
• Linear transformations on symmetric matrices that preserve commutativity
• Linear maps that preserve commuting pairs of matrices
• Invariants of linear maps on matrix algebras
• Pairs of quadratic forms
• Unnamed Item