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Miniversal deformations of pairs of skew-symmetric matrices under congruence
Department of Computing Science, Umeå University, Umeå, Sweden.ORCID-id: 0000-0001-9110-6182
2016 (engelsk)Inngår i: Linear Algebra and its Applications, ISSN 0024-3795, E-ISSN 1873-1856, Vol. 506, s. 506-534Artikkel i tidsskrift (Fagfellevurdert) Published
Abstract [en]

Miniversal deformations for pairs of skew-symmetric matrices under congruence are constructed. To be precise, for each such a pair (A, B) we provide a normal form with a minimal number of independent parameters to which all pairs of skew-symmetric matrices ((A) over tilde (,) (B) over tilde), close to (A, B) can be reduced by congruence transformation which smoothly depends on the entries of the matrices in the pair ((A) over tilde (,) (B) over tilde). An upper bound on the distance from such a miniversal deformation to (A, B) is derived too. We also present an example of using miniversal deformations for analyzing changes in the canonical structure information (i.e. eigenvalues and minimal indices) of skew-symmetric matrix pairs under perturbations.

sted, utgiver, år, opplag, sider
2016. Vol. 506, s. 506-534
Emneord [en]
Skew-symmetric matrix pair, Skew-symmetric matrix pencil, Congruence canonical form, Congruence, Perturbation, Versal deformation
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Identifikatorer
URN: urn:nbn:se:oru:diva-74874DOI: 10.1016/j.laa.2016.06.015ISI: 000381954300024Scopus ID: 2-s2.0-84974824043OAI: oai:DiVA.org:oru-74874DiVA, id: diva2:1332895
Tilgjengelig fra: 2019-06-28 Laget: 2019-06-28 Sist oppdatert: 2019-12-19bibliografisk kontrollert

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