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Miniversal deformations of pairs of symmetric matrices under congruence
Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för datavetenskap.
2019 (engelsk)Inngår i: Linear Algebra and its Applications, ISSN 0024-3795, E-ISSN 1873-1856, Vol. 568, s. 84-105Artikkel i tidsskrift (Fagfellevurdert) 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.

sted, utgiver, år, opplag, sider
Elsevier, 2019. Vol. 568, s. 84-105
Emneord [en]
Symmetric matrix pair, Symmetric matrix pencil, Congruence canonical form, Perturbation, Versal formation, Codimension
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Identifikatorer
URN: urn:nbn:se:umu:diva-157936DOI: 10.1016/j.laa.2018.05.034ISI: 000462111400005OAI: oai:DiVA.org:umu-157936DiVA, id: diva2:1305780
Tilgjengelig fra: 2019-04-18 Laget: 2019-04-18 Sist oppdatert: 2019-04-18bibliografisk kontrollert

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