Versal deformations: a tool of linear algebra

Abstract

A versal deformation of a matrix $A$ is a normal form to which all matrices $A+E$, close to $A$, can be reduced by similarity transformation smoothly depending on the entries of $A+E$. In this paper, we discuss versal deformations and their use in codimension computations, in investigation of closure relations of orbits and bundles, in studying changes of canonical forms under perturbations, as well as in the reduction of unstructured perturbations to structured perturbations.