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arXiv · 1308.5560

Determinantal Representations and Bézoutians

Mario Kummer
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Abstract

We show that for every smooth hyperbolic polynomial h there is another hyperbolic polynomial q such that qh has a definite determinantal representation. This is proved by considering sum-of-squares decompositions of certain bilinear forms called Bézoutians. Besides commutative algebra, the proof relies on results from real algebraic geometry.

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Mario Kummer. 2015-06-03. Determinantal Representations and Bézoutians. https://doi.org/10.1007/s00209-016-1715-9

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