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

  • O. M. Klymenko

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.
Published
25.09.2014
How to Cite
KlymenkoO. M. “Holomorphic Transformation to a Miniversal Deformation Not Always Exists Under *Congruence”. Ukrains’kyi Matematychnyi Zhurnal, Vol. 66, no. 9, Sept. 2014, pp. 1276–1279, http://umj.imath.kiev.ua/index.php/umj/article/view/2219.
Section
Short communications