Miniversal deformations of matrices of bilinear forms
Representation Theory
2012-12-14 v3
Abstract
V.I. Arnold [Russian Math. Surveys 26 (2) (1971) 29-43] constructed a miniversal deformation of matrices 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 construct a miniversal deformation of matrices under congruence.
Keywords
Cite
@article{arxiv.1004.3584,
title = {Miniversal deformations of matrices of bilinear forms},
author = {Andrii R. Dmytryshyn and Vyacheslav Futorny and Vladimir V. Sergeichuk},
journal= {arXiv preprint arXiv:1004.3584},
year = {2012}
}
Comments
39 pages. The first version of this paper was published as Preprint RT-MAT 2007-04, Universidade de Sao Paulo, 2007, 34 p. The work was done while the second author was visiting the University of Sao Paulo supported by the Fapesp grants (05/59407-6 and 2010/07278-6). arXiv admin note: substantial text overlap with arXiv:1105.2160