# On the reduction of matrix polynomials to Hessenberg form

@article{Cameron2016OnTR,
title={On the reduction of matrix polynomials to Hessenberg form},
author={Thomas R. Cameron},
journal={Electronic Journal of Linear Algebra},
year={2016},
volume={31},
pages={321-334}
}
• T. R. Cameron
• Published 5 February 2016
• Mathematics
• Electronic Journal of Linear Algebra
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…
2 Citations
Reduction of Matrix Polynomials to Simpler Forms
• Computer Science, Mathematics
SIAM J. Matrix Anal. Appl.
• 2018
This work introduces a practical means to reduce a matrix polynomial with nonsingular leading coefficient to a simpler (diagonal, triangular, Hessenberg) form while preserving the degree and the eigenstructure.
On the application of Laguerre's method to the polynomial eigenvalue problem
• Computer Science, Mathematics
• 2017
An effective method based on the numerical range is presented for computing initial estimates to the eigenvalues of a matrix polynomial and its competitiveness for solving the roots of a polynomials and the tridiagonal eigenvalue problem is verified.

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