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

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Ukrainian Mathematical Journal Aims and scope

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.

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Authors and Affiliations

  1. Kyiv Polytechnic Institute, Ukrainian National Technical University, Kyiv, Ukraine

    O. M. Klymenko

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  1. O. M. Klymenko
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Translated from Ukrains’kyi Matematychnyi Zhurnal, Vol. 66, No. 9, pp. 1276–1279, September, 2014

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Klymenko, O.M. Holomorphic Transformation to a Miniversal Deformation not Always Exists Under *Congruence. Ukr Math J 66, 1431–1434 (2015). https://doi.org/10.1007/s11253-015-1022-3

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  • DOI: https://doi.org/10.1007/s11253-015-1022-3

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