2017•arXiv (Cornell University)Open access
Companion matrix polynomials
A. Melman
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Abstract
We derive, from a given matrix polynomial, a lower order matrix polynomial with the same eigenvalues, which we call a companion matrix polynomial in analogy to the Frobenius companion matrix, which is a special case of our result. We derive a few nonstandard bounds on the zeros and eigenvalues of scalar and matrix polynomials, respectively, as an illustration of the usefulness of companion matrix polynomials.