Том 71
№ 9

All Issues

Klymenko O. M.

Articles: 1
Brief Communications (Ukrainian)

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

Klymenko O. M.

↓ Abstract   |   Full text (.pdf)

Ukr. Mat. Zh. - 2014. - 66, № 9. - pp. 1276–1279

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.