Student Co-author

Pomona Undergraduate

Document Type

Article - preprint


Mathematics (Pomona)

Publication Date



Complex symmetric matrix, Complex symmetric operator, Unitary equivalence, Unitary similarity, Unitary orbit, Transpose, Trace, Nilpotent, Truncated Toeplitz operator, UECSM, Words, SU(p, q)


A matrix TMn(C) is 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 4×4 nilpotent matrices which are UECSM and we settle an open problem which has lingered in the 3×3 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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Final publication can be found at:

Stephan Ramon Garcia, Daniel E. Poore, James E. Tener, Unitary equivalence to a complex symmetric matrix: Low dimensions, Linear Algebra and its Applications, Volume 437, Issue 1, 1 July 2012, Pages 271-284, ISSN 0024-3795, (

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© 2012 Elsevier B.V.

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