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arXiv · 0908.2107

Unitary equivalence of a matrix to its transpose

Stephan Ramon Garcia·James E. Tener
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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.

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Stephan Ramon Garcia, James E. Tener. 2009-08-14. Unitary equivalence of a matrix to its transpose. https://arxiv.org/abs/0908.2107

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