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Miniversal deformations of pairs of skew-symmetric matrices under congruence
Umeå University, Faculty of Science and Technology, Department of Computing Science.
2016 (English)In: Linear Algebra and its Applications, ISSN 0024-3795, E-ISSN 1873-1856, Vol. 506, p. 506-534Article in journal (Refereed) 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.

Place, publisher, year, edition, pages
2016. Vol. 506, p. 506-534
Keywords [en]
Skew-symmetric matrix pair, Skew-symmetric matrix pencil, Congruence canonical form, Congruence, Perturbation, Versal deformation
National Category
Mathematical Analysis
Identifiers
URN: urn:nbn:se:umu:diva-127581DOI: 10.1016/j.laa.2016.06.015ISI: 000381954300024OAI: oai:DiVA.org:umu-127581DiVA, id: diva2:1055838
Available from: 2016-12-13 Created: 2016-11-16 Last updated: 2018-06-09Bibliographically approved

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Dmytryshyn, Andrii

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