Unitary equivalence to a complex symmetric matrix: low dimensions

Unitary equivalence to a complex symmetric matrix: low dimensions

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 whic...

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Veröffentlicht in:arXiv.org 2012-01
Hauptverfasser: Stephan Ramon Garcia, Poore, Daniel E, Tener, James E
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Equivalence
Mathematical analysis
Matrix methods
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description 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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subjects Equivalence
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Matrix methods
title Unitary equivalence to a complex symmetric matrix: low dimensions
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