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

10 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

Access to Document

10.1016/j.laa.2012.01.029

Cite this

@article{9b12ac335f8340fd8eedbeca0046bab7,

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.",

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

author = "Garcia, {Stephan Ramon} and Poore, {Daniel E.} and Tener, {James E.}",

year = "2012",

month = jul,

day = "1",

doi = "10.1016/j.laa.2012.01.029",

language = "English",

volume = "437",

pages = "271--284",

journal = "Linear Algebra and Its Applications",

issn = "0024-3795",

publisher = "Elsevier Inc.",

number = "1",

}

TY - JOUR

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

UR - http://www.scopus.com/inward/record.url?scp=84859558557&partnerID=8YFLogxK

U2 - 10.1016/j.laa.2012.01.029

DO - 10.1016/j.laa.2012.01.029

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

Access to Document

Other files and links

Fingerprint

Cite this