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 naive assertion that a matrix is UET if and only if it is unitarily equivalent to a complex symmetric matrix (i.e., $T = T^t$) holds for matrices 7x7 and smaller, but fails for matrices 8x8 and larger.
 Publication:

arXiv eprints
 Pub Date:
 August 2009
 arXiv:
 arXiv:0908.2107
 Bibcode:
 2009arXiv0908.2107G
 Keywords:

 Mathematics  Functional Analysis;
 Mathematics  Operator Algebras;
 15A57;
 47A30
 EPrint:
 22 pages