On similarity invariants of matrix commutators and Jordan products

• Type: Article in International Scientific Journal
• Date: 2005

Authors

Susana Borges Furtado (Author) FEP; Enide Martins (Author) Other; Fernando Silva (Author) Other

Journal

Title: Linear Algebra and Its Applications

Vol. 401

Pages: 453-466

ISSN: 0024-3795

Publisher: Elsevier

Indexing

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Scientific classification

FOS: Natural sciences

Other information

Authenticus ID: P-000-3C4

DOI: 10.1016/j.laa.2004.12.011

Abstract (EN): 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, X-1], X-2], ..., X-k], when A is a fixed matrix and X-1, ... , X-k vary, were studied. Moreover given any expression 9(XI, - - -, Xk), obtained from distinct noncommuting variables X1, ... , X-k 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(X-1, ... , X-k) when one of the variables X-1, ... ,X-k takes a fixed value in F-nxn and the others vary, were studied.

Language: English

Type (Professor's evaluation): Scientific

No. of pages: 14