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Miniversal deformations of pairs of symmetric matrices under congruence
Department of Computing Science, Umeå University, Umeå, Sweden.ORCID iD: 0000-0001-9110-6182
2019 (English)In: Linear Algebra and its Applications, ISSN 0024-3795, E-ISSN 1873-1856, Vol. 568, p. 84-105Article in journal (Refereed) Published
Abstract [en]

For each pair of complex symmetric matrices (A, B) we provide a normal form with a minimal number of independent parameters, to which all pairs of complex symmetric matrices ((A) over tilde (B) over tilde), close to (A, B) can be reduced by congruence transformation that smoothly depends on the entries of (A ) over tilde and (B) over tilde. Such a normal form is called a miniversal deformation of (A, B) under congruence. A number of independent parameters in the miniversal deformation of a symmetric matrix pencil is equal to the codimension of the congruence orbit of this symmetric matrix pencil and is computed too. We also provide an upper bound on the distance from (A, B) to its miniversal deformation.

Place, publisher, year, edition, pages
Elsevier , 2019. Vol. 568, p. 84-105
Keywords [en]
Symmetric matrix pair, Symmetric matrix pencil, Congruence canonical form, Perturbation, Versal formation, Codimension
National Category
Mathematical Analysis
Identifiers
URN: urn:nbn:se:oru:diva-74875DOI: 10.1016/j.laa.2018.05.034ISI: 000462111400005Scopus ID: 2-s2.0-85048551989OAI: oai:DiVA.org:oru-74875DiVA, id: diva2:1332912
Available from: 2019-06-28 Created: 2019-06-28 Last updated: 2019-09-20Bibliographically approved

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Dmytryshyn, Andrii

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  • de-DE
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  • en-US
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  • nn-NO
  • nn-NB
  • sv-SE
  • Other locale
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Output format
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  • text
  • asciidoc
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