2017
Том 69
№ 7

All Issues

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

Klymenko O. M.

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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.

English version (Springer): Ukrainian Mathematical Journal 66 (2014), no. 9, pp 1431-1434.

Citation Example: Klymenko O. M. Holomorphic Transformation to a Miniversal Deformation not Always Exists Under *Congruence // Ukr. Mat. Zh. - 2014. - 66, № 9. - pp. 1276–1279.

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