oru.sePublikationer
Ändra sökning
RefereraExporteraLänk till posten
Permanent länk

Direktlänk
Referera
Referensformat
  • apa
  • ieee
  • modern-language-association-8th-edition
  • vancouver
  • Annat format
Fler format
Språk
  • de-DE
  • en-GB
  • en-US
  • fi-FI
  • nn-NO
  • nn-NB
  • sv-SE
  • Annat språk
Fler språk
Utmatningsformat
  • html
  • text
  • asciidoc
  • rtf
Change of the congruence canonical form of 2-by-2 and 3-by-3 matrices under perturbations and bundles of matrices under congruence
Department of Computing Science and HPC2N, Umeå University, Umeå, Sweden.ORCID-id: 0000-0001-9110-6182
Department of Mathematics, University of São Paulo, São Paulo, Brazil.
Department of Computing Science and HPC2N, Umeå University, Umeå, Sweden.
National Technical University of Ukraine “Kyiv Polytechnic Institute”, Kiev, Ukraine.
Visa övriga samt affilieringar
2015 (Engelska)Ingår i: Linear Algebra and its Applications, ISSN 0024-3795, E-ISSN 1873-1856, Vol. 469, s. 305-334Artikel i tidskrift (Refereegranskat) Published
Abstract [en]

We construct the Hasse diagrams G2 and G3 for the closure ordering on the sets of congruence classes of 2 × 2 and 3 × 3 complex matrices. In other words, we construct two directed graphs whose vertices are 2 × 2 or, respectively, 3 × 3 canonical matrices under congruence, and there is a directed path from A to B if and only if A can be transformed by an arbitrarily small perturbation to a matrix that is congruent to B. A bundle of matrices under congruence is defined as a set of square matrices A for which the pencils A + λAT belong to the same bundle under strict equivalence. In support of this definition, we show that all matrices in a congruence bundle of 2 × 2 or 3 × 3 matrices have the same properties with respect to perturbations. We construct the Hasse diagrams G2 B and G3 B for the closure ordering on the sets of congruence bundles of 2 × 2 and, respectively, 3 × 3 matrices. We find the isometry groups of 2 × 2 and 3 × 3 congruence canonical matrices.

Ort, förlag, år, upplaga, sidor
Elsevier, 2015. Vol. 469, s. 305-334
Nyckelord [en]
Bundle, Closure graph, Congruence canonical form, Congruence class, Perturbation
Nationell ämneskategori
Matematisk analys
Forskningsämne
matematik; administrativ databehandling
Identifikatorer
URN: urn:nbn:se:oru:diva-74885DOI: 10.1016/j.laa.2014.11.004ISI: 000348883600014Scopus ID: 2-s2.0-84919935890OAI: oai:DiVA.org:oru-74885DiVA, id: diva2:1332901
Forskningsfinansiär
eSSENCE - An eScience CollaborationVetenskapsrådet, A0581501Tillgänglig från: 2019-06-28 Skapad: 2019-06-28 Senast uppdaterad: 2019-09-20Bibliografiskt granskad

Open Access i DiVA

Fulltext saknas i DiVA

Övriga länkar

Förlagets fulltextScopus

Personposter BETA

Dmytryshyn, AndriiKågström, Bo

Sök vidare i DiVA

Av författaren/redaktören
Dmytryshyn, AndriiKågström, Bo
I samma tidskrift
Linear Algebra and its Applications
Matematisk analys

Sök vidare utanför DiVA

GoogleGoogle Scholar

doi
urn-nbn

Altmetricpoäng

doi
urn-nbn
Totalt: 71 träffar
RefereraExporteraLänk till posten
Permanent länk

Direktlänk
Referera
Referensformat
  • apa
  • ieee
  • modern-language-association-8th-edition
  • vancouver
  • Annat format
Fler format
Språk
  • de-DE
  • en-GB
  • en-US
  • fi-FI
  • nn-NO
  • nn-NB
  • sv-SE
  • Annat språk
Fler språk
Utmatningsformat
  • html
  • text
  • asciidoc
  • rtf