Hermitian matrices with a bounded number of eigenvalues |
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Authors: | M Domokos |
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Institution: | Rényi Institute of Mathematics, Hungarian Academy of Sciences, 1053 Budapest, Reáltanoda utca 13-15, Hungary |
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Abstract: | Conjugation covariants of matrices are applied to study the real algebraic variety consisting of complex Hermitian matrices with a bounded number of distinct eigenvalues. A minimal generating system of the vanishing ideal of degenerate three by three Hermitian matrices is given, and the structure of the corresponding coordinate ring as a module over the special unitary group is determined. The method applies also for degenerate real symmetric three by three matrices. For arbitrary n partial information on the minimal degree component of the vanishing ideal of the variety of n×n Hermitian matrices with a bounded number of eigenvalues is obtained, and some known results on sum of squares presentations of subdiscriminants of real symmetric matrices are extended to the case of complex Hermitian matrices. |
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Keywords: | primary 13F20 13A50 14P05 secondary 15A15 15A72 20G05 22E47 |
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