On similarity invariants of matrix commutators

We study the possible eigenvalues, ranks and numbers of nonconstant invariant polynomials of [⋯[[A,X 1],X 2],…,X k] , when A is a fixed matrix and X 1,…,X k vary. Then we generalize these results in the following way. Let g(X 1,…, X k) be any expression obtained from distinct noncommuting variables...

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Bibliographic Details
Published inLinear algebra and its applications Vol. 335; no. 1; pp. 81 - 93
Main Authors Furtado, Susana, Martins, Enide Andrade, Silva, Fernando C.
Format Journal Article
LanguageEnglish
Published New York, NY Elsevier Inc 15.09.2001
Elsevier Science
Subjects
Algebra
Exact sciences and technology
Linear and multilinear algebra, matrix theory
Linear and multilinear algebra, matrix theory (finite and infinite)
Logic, set theory, and algebra
Mathematical methods in physics
Mathematics
Physics
Sciences and techniques of general use
Matrix calculus
Invariant
Mathematical commutator
Eigenvalue problem
Similarity solution
Similarity
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Summary:We study the possible eigenvalues, ranks and numbers of nonconstant invariant polynomials of [⋯[[A,X 1],X 2],…,X k] , when A is a fixed matrix and X 1,…,X k vary. Then we generalize these results in the following way. Let g(X 1,…, X k) be any expression obtained from distinct noncommuting variables X 1,…,X k by applying recursively the Lie product [· ,·] and without using the same variable twice. We study the possible eigenvalues, ranks and numbers of nonconstant invariant polynomials of g(X 1,…,X k) when one of the variables X 1,…,X k takes a fixed value in F n×n and the others vary.
ISSN:0024-3795
1873-1856
DOI:10.1016/S0024-3795(00)00334-7