Garcia, Stephan RamonTener, James E.2025-05-302025-05-300379-4024http://www.scopus.com/inward/record.url?scp=84871364408&partnerID=8YFLogxKhttps://hdl.handle.net/1885/733754740Motivated by a problem of Halmos, we obtain a canonical decomposition for complex matrices which are unitarily equivalent to their transpose (UET). Surprisingly, the naïve assertion that a matrix is UET if and only if it is unitarily equivalent to a complex symmetric matrix holds for matrices 7 × 7 and smaller, but fails for matrices 8 × 8 and larger.25enComplex symmetric matrixComplex symmetric operatorLinear preserverNumerical rangeSkew-HamiltonianTransposeUECSMUnitary equivalenceUnitary orbit201284871364408