Polyhedral faces in Gram spectrahedra of binary forms

No Thumbnail Available
Files
There are no files associated with this item.
Date
2021
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
Linear Algebra and Its Applications ; 608 (2021). - pp. 133-157. - Elsevier. - ISSN 0024-3795. - eISSN 1873-1856
Abstract
The positive semidefinite Gram matrices of a form f with real coefficients parametrize the sum-of-squares representations of f. The convex body formed by the entirety of these matrices is the so-called Gram spectrahedron of f. We analyze the facial structures of symmetric and Hermitian Gram spectrahedra in the case of binary forms. We give upper bounds for the dimensions of polyhedral faces in Hermitian Gram spectrahedra and show that, if the form f is sufficiently generic, they can be realized by faces that are simplices and whose extreme points are rank-one tensors. We use our construction to prove a similar statement for the real symmetric case.
Summary in another language
Subject (DDC)
510 Mathematics
Keywords
Convex algebraic geometry; Sums of squares; Spectrahedra; Face; Binary form; Polyhedra
Conference
Review
undefined / . - undefined, undefined. - (undefined; undefined)
Cite This
ISO 690MAYER, Thorsten, 2021. Polyhedral faces in Gram spectrahedra of binary forms. In: Linear Algebra and Its Applications. Elsevier. 608, pp. 133-157. ISSN 0024-3795. eISSN 1873-1856. Available under: doi: 10.1016/j.laa.2020.08.025
BibTex
@article{Mayer2021Polyh-51726,
  year={2021},
  doi={10.1016/j.laa.2020.08.025},
  title={Polyhedral faces in Gram spectrahedra of binary forms},
  volume={608},
  issn={0024-3795},
  journal={Linear Algebra and Its Applications},
  pages={133--157},
  author={Mayer, Thorsten}
}
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/123456789/51726">
    <foaf:homepage rdf:resource="http://localhost:8080/"/>
    <dc:language>eng</dc:language>
    <void:sparqlEndpoint rdf:resource="http://localhost/fuseki/dspace/sparql"/>
    <dc:creator>Mayer, Thorsten</dc:creator>
    <dcterms:available rdf:datatype="http://www.w3.org/2001/XMLSchema#dateTime">2020-11-11T08:14:38Z</dcterms:available>
    <dc:date rdf:datatype="http://www.w3.org/2001/XMLSchema#dateTime">2020-11-11T08:14:38Z</dc:date>
    <dc:contributor>Mayer, Thorsten</dc:contributor>
    <dcterms:isPartOf rdf:resource="https://kops.uni-konstanz.de/server/rdf/resource/123456789/39"/>
    <dcterms:title>Polyhedral faces in Gram spectrahedra of binary forms</dcterms:title>
    <dcterms:issued>2021</dcterms:issued>
    <dspace:isPartOfCollection rdf:resource="https://kops.uni-konstanz.de/server/rdf/resource/123456789/39"/>
    <dcterms:abstract xml:lang="eng">The positive semidefinite Gram matrices of a form f with real coefficients parametrize the sum-of-squares representations of f. The convex body formed by the entirety of these matrices is the so-called Gram spectrahedron of f. We analyze the facial structures of symmetric and Hermitian Gram spectrahedra in the case of binary forms. We give upper bounds for the dimensions of polyhedral faces in Hermitian Gram spectrahedra and show that, if the form f is sufficiently generic, they can be realized by faces that are simplices and whose extreme points are rank-one tensors. We use our construction to prove a similar statement for the real symmetric case.</dcterms:abstract>
    <bibo:uri rdf:resource="https://kops.uni-konstanz.de/handle/123456789/51726"/>
  </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
Yes
Refereed
Yes