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Miniversal deformations of matrices under *congruence and reducing transformations
Department of Computing Science and HPC2N, Umeå University, Umeå, Sweden.
Department of Mathematics, University of São Paulo, São 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, p. 388-420Article 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, p. 388-420
National Category
Mathematical Analysis
Research subject
Mathematics
Identifiers
URN: urn:nbn:se:oru:diva-74887DOI: 10.1016/j.laa.2014.01.016ISI: 000334146700027Scopus ID: 2-s2.0-84894271676OAI: oai:DiVA.org:oru-74887DiVA, id: diva2:1332903
Funder
eSSENCE - An eScience CollaborationSwedish Research Council, A0581501Available from: 2019-06-28 Created: 2019-06-28 Last updated: 2019-07-05Bibliographically approved

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  • nn-NB
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  • Other locale
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