  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.

Representation Theory