On Matrix Polynomials with Real Roots

Details On Matrix Polynomials with Real Roots On Matrix Polynomials with Real Roots

2004-06-21

arxiv.org/abs/math/0406419v1

Mathematics

Optimization and Control

9 pages, submitted

Scientific paper

It is proved that the roots of combinations of matrix polynomials with real
roots can be recast as eigenvalues of combinations of real symmetric matrices,
under certain hypotheses. The proof is based on recent solution of the Lax
conjecture. Several applications and corollaries, in particular concerning
hyperbolic matrix polynomials, are presented.

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