Publikation: Determinantal representations and Bézoutians
Lade...
Dateien
Zu diesem Dokument gibt es keine Dateien.
Datum
2017
Autor:innen
Herausgeber:innen
ISSN der Zeitschrift
Electronic ISSN
ISBN
Bibliografische Daten
Verlag
Schriftenreihe
Auflagebezeichnung
DOI (zitierfähiger Link)
Internationale Patentnummer
Angaben zur Forschungsförderung
Projekt
Open Access-Veröffentlichung
Sammlungen
Core Facility der Universität Konstanz
Titel in einer weiteren Sprache
Publikationstyp
Zeitschriftenartikel
Publikationsstatus
Published
Erschienen in
Mathematische Zeitschrift. 2017, 285(1-2), pp. 445-459. ISSN 0025-5874. eISSN 1432-1823. Available under: doi: 10.1007/s00209-016-1715-9
Zusammenfassung
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.
Zusammenfassung in einer weiteren Sprache
Fachgebiet (DDC)
510 Mathematik
Schlagwörter
Konferenz
Rezension
undefined / . - undefined, undefined
Zitieren
ISO 690
KUMMER, Mario, 2017. Determinantal representations and Bézoutians. In: Mathematische Zeitschrift. 2017, 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}
}RDF
<rdf:RDF
xmlns:dcterms="http://purl.org/dc/terms/"
xmlns:dc="http://purl.org/dc/elements/1.1/"
xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#"
xmlns:bibo="http://purl.org/ontology/bibo/"
xmlns:dspace="http://digital-repositories.org/ontologies/dspace/0.1.0#"
xmlns:foaf="http://xmlns.com/foaf/0.1/"
xmlns:void="http://rdfs.org/ns/void#"
xmlns:xsd="http://www.w3.org/2001/XMLSchema#" >
<rdf:Description rdf:about="https://kops.uni-konstanz.de/server/rdf/resource/123456789/37954">
<dc:contributor>Kummer, Mario</dc:contributor>
<dcterms:title>Determinantal representations and Bézoutians</dcterms:title>
<foaf:homepage rdf:resource="http://localhost:8080/"/>
<dcterms:isPartOf rdf:resource="https://kops.uni-konstanz.de/server/rdf/resource/123456789/39"/>
<dcterms:available rdf:datatype="http://www.w3.org/2001/XMLSchema#dateTime">2017-03-10T13:43:27Z</dcterms:available>
<dc:creator>Kummer, Mario</dc:creator>
<dcterms:issued>2017-02</dcterms:issued>
<void:sparqlEndpoint rdf:resource="http://localhost/fuseki/dspace/sparql"/>
<dspace:isPartOfCollection rdf:resource="https://kops.uni-konstanz.de/server/rdf/resource/123456789/39"/>
<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>
<dc:date rdf:datatype="http://www.w3.org/2001/XMLSchema#dateTime">2017-03-10T13:43:27Z</dc:date>
<bibo:uri rdf:resource="https://kops.uni-konstanz.de/handle/123456789/37954"/>
<dc:language>eng</dc:language>
</rdf:Description>
</rdf:RDF>
