Invertibility of linear maps preserving matrix invariants

DOI10.1080/03081088308817510zbMath0516.15007OpenAlexW2063188904MaRDI QIDQ3663449

William C. Waterhouse

Publication date: 1983

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

Full work available at URL: https://doi.org/10.1080/03081088308817510

zbMATH Keywords

group of linear transformationsradicalsemi- groupinvertibility of linear mapssimilarity invariants of matrices

Mathematics Subject Classification ID

Determinants, permanents, traces, other special matrix functions (15A15) Vector and tensor algebra, theory of invariants (15A72) Algebraic systems of matrices (15A30) Linear transformations, semilinear transformations (15A04)

Related Items

Linear preservers for the \(q\)-permanent, cycle \(q\)-permanent expansions, and positive crossings in digraphs, Automorphisms of \(\det (X_{ij}):\) The group scheme approach, Linear preservers and representations with a 1-dimensional ring of invariants, Linear transformations on symmetric matrices II, Linear maps preserving rank less than or equal to one, Chapter 2:rank and tensor rank, Chapter 4:algebraic sets, polynomials, and other functions, Chapter 8: invariant preserving linear matrix mappings over rings and related topics, Invertible Preservers and Algebraic Groups II: Preservers of Similarity Invariants and Overgroups ofPSL_n(F), Automorphism Group Schemes of Basic Matrix Invariants, Linear preservers of rank permutability, Overgroups of $E(m,R)⊗E(n,R)$ I. Levels and normalizers, Linear transformations that preserve immanants

Cites Work

• Cohomology of split group extensions
• Representations of Algebraic Groups
• Linear Transformations on Algebras of Matrices: The Invariance of the Elementary Symmetric Functions
• The Permanent Function
• Linear Operations on Matrices
• Discriminant preserving linear maps
• Trace preserving linear transformations on matrix algebras
• Linear Transformations on Matrices: the Invariance of the Third Elementary Symmetric Function