Determinantal representations and Bézoutians


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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

@article{Kummer2017-02Deter-37954, title={Determinantal representations and Bézoutians}, year={2017}, doi={10.1007/s00209-016-1715-9}, number={1-2}, volume={285}, issn={0025-5874}, journal={Mathematische Zeitschrift}, pages={445--459}, author={Kummer, Mario} }

<rdf:RDF xmlns:rdf="" xmlns:bibo="" xmlns:dc="" xmlns:dcterms="" xmlns:xsd="" > <rdf:Description rdf:about=""> <dcterms:issued>2017-02</dcterms:issued> <dcterms:title>Determinantal representations and Bézoutians</dcterms:title> <dc:language>eng</dc:language> <dcterms:abstract xml:lang="eng">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.</dcterms:abstract> <bibo:uri rdf:resource=""/> <dcterms:available rdf:datatype="">2017-03-10T13:43:27Z</dcterms:available> <dc:date rdf:datatype="">2017-03-10T13:43:27Z</dc:date> <dc:creator>Kummer, Mario</dc:creator> <dc:contributor>Kummer, Mario</dc:contributor> </rdf:Description> </rdf:RDF>

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