Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Unitary equivalence of a matrix to its transpose   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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The categories of this paper are: plasm-ph
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The categories of this paper are: q-alg
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The categories of this paper are: dg-ga
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The categories of this paper are: nucl-th
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The categories of this paper are: quant-ph
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The categories of this paper are: cond-mat
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The categories of this paper are: ao-sci
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The categories of this paper are: solv-int
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The categories of this paper are: hep-ex
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The categories of this paper are: nucl-ex
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The categories of this paper are: alg-geom
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The categories of this paper are: adap-org
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The categories of this paper are: gr-qc
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The categories of this paper are: econ
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The categories of this paper are: chem-ph
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The categories of this paper are: nlin