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 On similarity invariants of matrix commutators and Jordan products
Please use this identifier to cite or link to this item http://hdl.handle.net/10773/4283

title: On similarity invariants of matrix commutators and Jordan products
authors: Furtado, S.
Martins, E.A.
Silva, F.C.
issue date: 2005
publisher: Elsevier
abstract: Denote by [X, Y] the additive commutator XY - YX of two square matrices X, Y over a field F. In a previous paper, the possible eigenvalues, ranks and numbers of nonconstant invariant polynomials of [⋯[[A, X1], X2], ⋯, Xk], when A is a fixed matrix and X 1, ⋯, Xk vary, were studied. Moreover given any expression g(X1, ⋯, Xk), obtained from distinct noncommuting variables X1, ⋯, Xk by applying recursively the Lie product [•, •] and without using the same variable twice, the possible eigenvalues, ranks and numbers of nonconstant invariant polynomials of g(X1, ⋯, Xk) when one of the variables X1, ⋯, Xk takes a fixed value in F n×n and the others vary, were studied. The purpose of the present paper is to show that analogous results can be obtained when additive commutators are replaced with multiplicative commutators or Jordan products. © 2005 Elsevier Inc. All rights reserved.
URI: http://hdl.handle.net/10773/4283
ISSN: 0024-3795
publisher version/DOI: http://www.sciencedirect.com/science/article/pii/S0024379504005208
source: Linear Algebra and Its Applications
appears in collectionsMAT - Artigos

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