Polyhedral faces in Gram spectrahedra of binary forms

Mayer, Thorsten

Polyhedral faces in Gram spectrahedra of binary forms

Dateien

Zu diesem Dokument gibt es keine Dateien.

Datum

2021

Publikationstyp

Zeitschriftenartikel

Publikationsstatus

Published

Erschienen in

Linear Algebra and Its Applications. Elsevier. 2021, 608, pp. 133-157. ISSN 0024-3795. eISSN 1873-1856. Available under: doi: 10.1016/j.laa.2020.08.025

Zusammenfassung

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.

Fachgebiet (DDC)

510 Mathematik

Schlagwörter

Convex algebraic geometry; Sums of squares; Spectrahedra; Face; Binary form; Polyhedra

Zitieren

ISO 690

MAYER, Thorsten, 2021. Polyhedral faces in Gram spectrahedra of binary forms. In: Linear Algebra and Its Applications. Elsevier. 2021, 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>

Universitätsbibliographie

Ja

Begutachtet

Ja