Spectrally arbitrary, nonderogatory factorization over a general field

It is known that a nonsingular, nonscalar matrix A , over the complex field, may be factored as A = BC , in which the spectra of B and C are arbitrary, subject to det B det C = det A , and that B and C may be taken to be nonderogatory. The purpose of this paper is to establish this result over a gen...

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Bibliographic Details
Published inLinear algebra and its applications Vol. 433; no. 1; pp. 1 - 11
Main Author Botha, J.D.
Format Journal Article
LanguageEnglish
Published Amsterdam Elsevier Inc 15.07.2010
Elsevier
Subjects
Algebra
Exact sciences and technology
Field theory and polynomials
Linear and multilinear algebra, matrix theory
Mathematics
Nonderogatory
Rational canonical form
Sciences and techniques of general use
Special [formula omitted] factorization
Spectrum
Rational canonical form
Special LU factorization
15A23
15A33
Nonderogatory
Spectrum
LU factorization
Ring
Matrix factorization
Field (mathematics)
Canonical form
Online AccessGet full text
ISSN0024-3795
DOI10.1016/j.laa.2010.01.029

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Summary:It is known that a nonsingular, nonscalar matrix A , over the complex field, may be factored as A = BC , in which the spectra of B and C are arbitrary, subject to det B det C = det A , and that B and C may be taken to be nonderogatory. The purpose of this paper is to establish this result over a general field with at least four elements.
ISSN:0024-3795
DOI:10.1016/j.laa.2010.01.029