Determinantal representations and Bézoutians

No Thumbnail Available
Files
There are no files associated with this item.
Date
2017
Editors
Contact
Journal ISSN
Electronic ISSN
ISBN
Bibliographical data
Publisher
Series
URI (citable link)
DOI (citable link)
ArXiv-ID
International patent number
Link to the license
oops
EU project number
Project
Open Access publication
Restricted until
Title in another language
Research Projects
Organizational Units
Journal Issue
Publication type
Journal article
Publication status
Published
Published in
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.
Summary in another language
Subject (DDC)
510 Mathematics
Keywords
Conference
Review
undefined / . - undefined, undefined. - (undefined; undefined)
Cite This
ISO 690KUMMER, 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/s00209-016-1715-9
BibTex
@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>
Internal note
xmlui.Submission.submit.DescribeStep.inputForms.label.kops_note_fromSubmitter
Contact
URL of original publication
Test date of URL
Examination date of dissertation
Method of financing
Comment on publication
Alliance license
Corresponding Authors der Uni Konstanz vorhanden
International Co-Authors
Bibliography of Konstanz
Refereed