Abstract
Let S1, S2, S3, S4 be given finite sets of pairs of n-by-n complex matrices. We describe an algorithm to determine, with finitely many computations, whether there is a single unitary matrix U such that each pair of matrices in S1 is unitarily similar via U, each pair of matrices in S2 is unitarily congruent via U, each pair of matrices in S3 is unitarily similar via U¯, and each pair of matrices in S4 is unitarily congruent via U¯.
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