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 ∈ Mn(ℂ) 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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