Unitary Equivalence of a Matrix to Its Transpose
unitarily equivalent to its transpose, complex symmetric matrix
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.
© 2012 Theta Foundation
Garcia, S.R., Tener, J.E., Unitary equivalence of a matrix to its transpose, J. Operator Theory 68 (2012), no. 1, 179-203. MR2966041