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Miniversal deformations of matrices under *congruence and reducing transformations
Umeå University, Faculty of Science and Technology, Department of Computing Science. Umeå University, Faculty of Science and Technology, High Performance Computing Center North (HPC2N). (UMIT)
University of Sao Paulo, Brazil .
Institute of Mathematics, Kiev, Ukraine.
2014 (English)In: Linear Algebra and its Applications, ISSN 0024-3795, E-ISSN 1873-1856, Vol. 446, no April, 388-420 p.Article in journal (Refereed) Published
Abstract [en]

Arnold (1971) [1] constructed a miniversal deformation of a square complex matrix under similarity; that is, a simple normal form to which not only a given square matrix A but all matrices B close to it can be reduced by similarity transformations that smoothly depend on the entries of B. We give miniversal deformations of matrices of sesquilinear forms; that is, of square complex matrices under *congruence, and construct an analytic reducing transformation to a miniversal deformation. Analogous results for matrices under congruence were obtained by Dmytryshyn, Futorny, and Sergeichuk (2012) [11].

Place, publisher, year, edition, pages
Elsevier, 2014. Vol. 446, no April, 388-420 p.
National Category
Natural Sciences Mathematics
Research subject
Mathematics
Identifiers
URN: urn:nbn:se:umu:diva-88006DOI: 10.1016/j.laa.2014.01.016ISI: 000334146700027OAI: oai:DiVA.org:umu-88006DiVA: diva2:713112
Funder
eSSENCE - An eScience CollaborationSwedish Research Council, A0581501
Available from: 2014-04-21 Created: 2014-04-21 Last updated: 2017-12-05Bibliographically approved

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Dmytryshyn, Andrii

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