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Unitary equivalence of a matrix to its transpose

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Date

2012

Authors

Garcia, Stephan Ramon
Tener, James E.

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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 naïve assertion that a matrix is UET if and only if it is unitarily equivalent to a complex symmetric matrix holds for matrices 7 × 7 and smaller, but fails for matrices 8 × 8 and larger.

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Complex symmetric matrix, Complex symmetric operator, Linear preserver, Numerical range, Skew-Hamiltonian, Transpose, UECSM, Unitary equivalence, Unitary orbit

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http://www.scopus.com/inward/record.url?scp=84871364408&partnerID=8YFLogxK
 https://hdl.handle.net/1885/733754740

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ANU Research Publications

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Journal of Operator Theory

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Journal article

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