On linear preservers of normal maps |
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Authors: | Marek Niezgoda |
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Affiliation: | Department of Applied Mathematics, Agricultural University in Lublin, P.O. Box 158, Akademicka 13, 20-950 Lublin, Poland |
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Abstract: | We study group induced cone (GIC) orderings generating normal maps. Examples of normal maps cover, among others, the eigenvalue map on the space of n × n Hermitian matrices as well as the singular value map on n × n complex matrices. In this paper, given two linear spaces equipped with GIC orderings induced by groups of orthogonal operators, we investigate linear operators preserving normal maps of the orderings. A characterization of the preservers is obtained in terms of the groups. The result is applied to show that the normal structure of the spaces is preserved under the action of the operators. In addition, examples are given. |
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Keywords: | 06F20 20F55 15A30 15A18 |
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