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arXiv · 1105.2160

Miniversal deformations of matrices under *congruence and reducing transformations

A. Dmytryshyn·V. Futorny·V. V. Sergeichuk
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Abstract

V.I. Arnold [Russian Math. Surveys 26(2) (1971) 29-43] 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 the authors in [Linear Algebra Appl. 436 (2012) 2670-2700].

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A. Dmytryshyn, V. Futorny, V. V. Sergeichuk. 2013-10-06. Miniversal deformations of matrices under *congruence and reducing transformations. https://doi.org/10.1016/j.laa.2014.01.016

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