Tener, James E.2025-05-302025-05-300022-247Xhttp://www.scopus.com/inward/record.url?scp=38749122092&partnerID=8YFLogxKhttps://hdl.handle.net/1885/733755442We 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.We wish to thank S.R. Garcia for his many valuable suggestions, continued support, and financial contribution via NSF Grant DMS 0638789.9enComplex symmetric matrixUnitary equivalence2008-05-0110.1016/j.jmaa.2007.10.02938749122092