Unitary equivalence of a matrix to its transpose

Details Unitary equivalence of a matrix to its transpose Unitary equivalence of a matrix to its transpose

2009-08-14

arxiv.org/abs/0908.2107v4

Mathematics

Functional Analysis

22 pages

Scientific paper

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.

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