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arXiv · 1104.4960

Unitary equivalence to a complex symmetric matrix: low dimensions

Stephan Ramon Garcia·Daniel E. Poore·James E. Tener
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Abstract

A matrix $T \in \M_n(\C)$ is \emph{UECSM} if it is unitarily equivalent to a complex symmetric (i.e., self-transpose) matrix. We develop several techniques for studying this property in dimensions three and four. Among other things, we completely characterize $4 \times 4$ nilpotent matrices which are UECSM and we settle an open problem which has lingered in the $3 \times 3$ case. We conclude with a discussion concerning a crucial difference which makes dimension three so different from dimensions four and above

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Stephan Ramon Garcia, Daniel E. Poore, James E. Tener. 2011-04-26. Unitary equivalence to a complex symmetric matrix: low dimensions. https://arxiv.org/abs/1104.4960

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