Determinantal representations and Bézoutians
Determinantal representations and Bézoutians
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2017
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Mathematische Zeitschrift ; 285 (2017), 1-2. - pp. 445-459. - ISSN 0025-5874. - eISSN 1432-1823
Abstract
A major open question in convex algebraic geometry is whether all hyperbolicity cones are spectrahedral, i.e. the solution sets of linear matrix inequalities. We will use sum-of-squares decompositions of certain bilinear forms called Bézoutians to approach this problem. More precisely, we show that for every smooth hyperbolic polynomial h there is another hyperbolic polynomial q such that q⋅h has a definite determinantal representation. Besides commutative algebra, the proof relies on results from real algebraic geometry.
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KUMMER, Mario, 2017. Determinantal representations and Bézoutians. In: Mathematische Zeitschrift. 285(1-2), pp. 445-459. ISSN 0025-5874. eISSN 1432-1823. Available under: doi: 10.1007/s00209-016-1715-9BibTex
@article{Kummer2017-02Deter-37954, year={2017}, doi={10.1007/s00209-016-1715-9}, title={Determinantal representations and Bézoutians}, number={1-2}, volume={285}, issn={0025-5874}, journal={Mathematische Zeitschrift}, pages={445--459}, author={Kummer, Mario} }
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