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arXiv · 1805.11580

Algebraic Linearizations of Matrix Polynomials

Eunice Y. S. Chan·Robert M. Corless·Laureano Gonzalez-Vega·J. Rafael Sendra·Juana Sendra
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Abstract

We show how to construct linearizations of matrix polynomials $z\mathbf{a}(z)\mathbf{d}_0 + \mathbf{c}_0$, $\mathbf{a}(z)\mathbf{b}(z)$, $\mathbf{a}(z) + \mathbf{b}(z)$ (when $\mathrm{deg}\left(\mathbf{b}(z)\right) < \mathrm{deg}\left(\mathbf{a}(z)\right)$), and $z\mathbf{a}(z)\mathbf{d}_0\mathbf{b}(z) + \mathbf{c_0}$ from linearizations of the component parts, $\mathbf{a}(z)$ and $\mathbf{b}(z)$. This allows the extension to matrix polynomials of a new companion matrix construction.

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Eunice Y. S. Chan, Robert M. Corless, Laureano Gonzalez-Vega, J. Rafael Sendra, Juana Sendra. 2018-05-29. Algebraic Linearizations of Matrix Polynomials. https://arxiv.org/abs/1805.11580

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