Unitary equivalence to a complex symmetric matrix

Abstract

We present a necessary and sufficient condition for a 3 × 3 matrix to be unitarily equivalent to a symmetric matrix with complex entries, and an algorithm whereby an arbitrary 3 × 3 matrix can be tested. This test generalizes to a necessary and sufficient condition that applies to almost every n × n matrix. The test is constructive in that it explicitly exhibits the unitary equivalence to a complex symmetric matrix. Show more