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Miniversal deformations of matrices under *congruence and reducing transformations
Department of Computing Science and HPC2N, Umeå University, Umeå, Sweden.ORCID iD: 0000-0001-9110-6182
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: 2019-09-20Bibliographically approved

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