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We present a necessary and sufficient condition for a 3 by 3 matrix to beunitarily equivalent to a symmetric matrix with complex entries, and analgorithm whereby an arbitrary 3 by 3 matrix can be tested. This testgeneralizes to a necessary and sufficient condition that applies to almostevery n by n matrix. The test is constructive in that it explicitly exhibitsthe unitary equivalence to a complex symmetric matrix.

Unitary equivalence to a complex symmetric matrix: an algorithm