Miniversal deformations of matrices under *congruence and reducing transformations
Representation Theory
2014-01-21 v3
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].
Cite
@article{arxiv.1105.2160,
title = {Miniversal deformations of matrices under *congruence and reducing transformations},
author = {A. Dmytryshyn and V. Futorny and V. V. Sergeichuk},
journal= {arXiv preprint arXiv:1105.2160},
year = {2014}
}
Comments
36 pages. arXiv admin note: text overlap with arXiv:1305.6675 by other authors