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arXiv · 1608.04204

About the solvability of matrix polynomial equations

Tim Netzer·Andreas Thom
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Abstract

We study self-adjoint matrix polynomial equations in a single variable and prove existence of self-adjoint solutions under some assumptions on the leading form. Our main result is that any self-adjoint matrix polynomial equation of odd degree with non-degenerate leading form can be solved in self-adjoint matrices. We also study equations of even degree and equations in many variables.

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Tim Netzer, Andreas Thom. 2016-08-15. About the solvability of matrix polynomial equations. https://arxiv.org/abs/1608.04204

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