Unitary equivalence of a matrix to its transpose

Abstract

Motivated 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. Show more