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.

22 pages

References in corpus (1)

• Unitary equivalence to a complex symmetric matrix: geometric criteria

Cited by in corpus (8)

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• Complex symmetry of Toeplitz operators
• Unitary equivalence to a truncated Toeplitz operator: analytic symbols