Miniversal deformations of matrices under *congruence and reducing transformations

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].

36 pages. arXiv admin note: text overlap with arXiv:1305.6675 by other authors

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Cited by in corpus (7)

• Miniversal deformations of matrices of bilinear forms
• Change of the congruence canonical form of 2-by-2 and 3-by-3 matrices under perturbations and bundles of matrices under congruence
• Neighborhood radius estimation for Arnold's miniversal deformations of complex and $p$-adic matrices
• An informal introduction to perturbations of matrices determined up to similarity or congruence
• A holomorphic transformation to a miniversal deformation under *congruence does not always exist
• Recovering a perturbation of a matrix polynomial from a perturbation of its linearization
• A constructive proof of Pokrzywa's theorem about perturbations of matrix pencils