On complex matrices that are unitarily similar to real matrices |
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Authors: | Kh D Ikramov |
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Institution: | 1. Moscow State University, Moscow, Russia
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Abstract: | There are well-known conditions ensuring that a complex n × n matrix A can be converted by a similarity transformation into a real matrix. Is it possible to realize this conversion via unitary similarity rather than a general one? The following answer to this question is given in this paper: A matrix A ∈ M n (?) can be made real by a unitary similarity transformation if and only if A and ā are unitarily similar and the matrix P transforming A into ā can be chosen unitary and symmetric at the same time. Effective ways for verifying this criterion are discussed. |
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