Holomorphic Transformation to a Miniversal Deformation not Always Exists Under *Congruence

Abstract

In 1971, Arnold constructed miniversal deformations of square complex matrices under the similarity transformation. Similar miniversal deformations were constructed for matrices under congruence and under *congruence. For matrices under similarity and under congruence, the holomorphic transformations to their miniversal deformations always exist. We prove that this is not true for matrices under *congruence.