On the reduction of matrix polynomials to hessenberg form

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Abstract

It is well known that every real or complex square matrix is unitarily similar to an upper Hessenberg matrix. The purpose of this paper is to provide a constructive proof of the result that every square matrix polynomial can be reduced to an upper Hessenberg matrix, whose entries are rational functions and in special cases polynomials. It will be shown that the determinant is preserved under this transformation, and both the finite and infinite eigenvalues of the original matrix polynomial can be obtained from the upper Hessenberg matrix.

Original languageEnglish (US)
Article number24
Pages (from-to)321-334
Number of pages14
JournalElectronic Journal of Linear Algebra
Volume31
Issue number1
DOIs
StatePublished - 2016

All Science Journal Classification (ASJC) codes

  • Algebra and Number Theory

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