## Pomona Faculty Publications and Research

#### Title

Unitary Equivalence of a Matrix to Its Transpose

Article

#### Department

Mathematics (Pomona)

2012

#### Keywords

unitarily equivalent to its transpose, complex symmetric matrix

#### 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 na\"ive assertion that a matrix is UET if and only if it is unitarily equivalent to a complex symmetric matrix holds for matrices $7 \times 7$ and smaller, but fails for matrices $8 \times 8$ and larger.