Unitary equivalence to a complex symmetric matrix: Low dimensions

Stephan Ramon Garcia; Daniel E. Poore; James E. Tener

doi:10.1016/j.laa.2012.01.029

Unitary equivalence to a complex symmetric matrix: Low dimensions

Stephan Ramon Garcia^*
, Daniel E. Poore
, James E. Tener

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

11 Citations (Scopus)

Abstract

A matrix T∈ ^Mn(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.

Original language	English
Pages (from-to)	271-284
Number of pages	14
Journal	Linear Algebra and Its Applications
Volume	437
Issue number	1
DOIs	https://doi.org/10.1016/j.laa.2012.01.029
Publication status	Published - 1 Jul 2012
Externally published	Yes

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title = "Unitary equivalence to a complex symmetric matrix: Low dimensions",

abstract = "A matrix T∈ Mn(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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T1 - Unitary equivalence to a complex symmetric matrix

T2 - Low dimensions

AU - Garcia, Stephan Ramon

AU - Poore, Daniel E.

AU - Tener, James E.

PY - 2012/7/1

Y1 - 2012/7/1

N2 - A matrix T∈ Mn(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.

AB - A matrix T∈ Mn(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.

KW - Complex symmetric matrix

KW - Complex symmetric operator

KW - Nilpotent

KW - SU (p, q)

KW - Trace

KW - Transpose

KW - Truncated Toeplitz operator

KW - UECSM

KW - Unitary equivalence

KW - Unitary orbit

KW - Unitary similarity

KW - Words

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M3 - Article

AN - SCOPUS:84859558557

SN - 0024-3795

VL - 437

SP - 271

EP - 284

JO - Linear Algebra and Its Applications

JF - Linear Algebra and Its Applications

IS - 1

ER -

Unitary equivalence to a complex symmetric matrix: Low dimensions

Abstract

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