On the Unitary Similarity of Matrix Families |
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Authors: | Al'pin Yu. A. Ikramov Kh. D. |
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Affiliation: | 1. Kazan State University, Russia 2. M. V. Lomonosov Moscow State University, Russia
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Abstract: | The classical Specht criterion for the unitary similarity between two complex n × n matrices is extended to the unitary similarity between two normal matrix sets of cardinality m. This property means that the algebra generated by a set is closed with respect to the conjugate transpose operation. Similar to the well-known result of Pearcy that supplements Specht's theorem, the proposed extension can be made a finite criterion. The complexity of this criterion depends on n as well as the length l of the algebras under analysis. For a pair of matrices, this complexity can be significantly lower than that of the Specht--Pearcy criterion. |
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