  The reductions of a square complex matrix A to its canonical forms under
transformations of similarity, congruence, or *congruence are unstable
operations: these canonical forms and reduction transformations depend
discontinuously on the entries of A. We survey results about their behavior
under perturbations of A and about normal forms of all matrices A+E in a
neighborhood of A with respect to similarity, congruence, or *congruence. These
normal forms are called miniversal deformations of A; they are not uniquely
determined by A+E, but they are simple and depend continuously on the entries
of E.
