Unitary equivalence to a complex symmetric matrix: An algorithm

James E. Tener

doi:10.1016/j.jmaa.2007.10.029

Unitary equivalence to a complex symmetric matrix: An algorithm

James E. Tener^*

^*Corresponding author for this work

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

20 Citations (Scopus)

Abstract

We present a necessary and sufficient condition for a 3 × 3 matrix to be unitarily equivalent to a symmetric matrix with complex entries, and an algorithm whereby an arbitrary 3 × 3 matrix can be tested. This test generalizes to a necessary and sufficient condition that applies to almost every n × n matrix. The test is constructive in that it explicitly exhibits the unitary equivalence to a complex symmetric matrix.

Original language	English
Pages (from-to)	640-648
Number of pages	9
Journal	Journal of Mathematical Analysis and Applications
Volume	341
Issue number	1
DOIs	https://doi.org/10.1016/j.jmaa.2007.10.029
Publication status	Published - 1 May 2008
Externally published	Yes

Access to Document

10.1016/j.jmaa.2007.10.029

Cite this

@article{409462f6daf444b08e4f8e3670762b6c,

title = "Unitary equivalence to a complex symmetric matrix: An algorithm",

abstract = "We present a necessary and sufficient condition for a 3 × 3 matrix to be unitarily equivalent to a symmetric matrix with complex entries, and an algorithm whereby an arbitrary 3 × 3 matrix can be tested. This test generalizes to a necessary and sufficient condition that applies to almost every n × n matrix. The test is constructive in that it explicitly exhibits the unitary equivalence to a complex symmetric matrix.",

keywords = "Complex symmetric matrix, Unitary equivalence",

author = "Tener, {James E.}",

year = "2008",

month = may,

day = "1",

doi = "10.1016/j.jmaa.2007.10.029",

language = "English",

volume = "341",

pages = "640--648",

journal = "Journal of Mathematical Analysis and Applications",

issn = "0022-247X",

publisher = "Academic Press Inc.",

number = "1",

}

TY - JOUR

T1 - Unitary equivalence to a complex symmetric matrix

T2 - An algorithm

AU - Tener, James E.

PY - 2008/5/1

Y1 - 2008/5/1

N2 - We present a necessary and sufficient condition for a 3 × 3 matrix to be unitarily equivalent to a symmetric matrix with complex entries, and an algorithm whereby an arbitrary 3 × 3 matrix can be tested. This test generalizes to a necessary and sufficient condition that applies to almost every n × n matrix. The test is constructive in that it explicitly exhibits the unitary equivalence to a complex symmetric matrix.

AB - We present a necessary and sufficient condition for a 3 × 3 matrix to be unitarily equivalent to a symmetric matrix with complex entries, and an algorithm whereby an arbitrary 3 × 3 matrix can be tested. This test generalizes to a necessary and sufficient condition that applies to almost every n × n matrix. The test is constructive in that it explicitly exhibits the unitary equivalence to a complex symmetric matrix.

KW - Complex symmetric matrix

KW - Unitary equivalence

UR - http://www.scopus.com/inward/record.url?scp=38749122092&partnerID=8YFLogxK

U2 - 10.1016/j.jmaa.2007.10.029

DO - 10.1016/j.jmaa.2007.10.029

M3 - Article

AN - SCOPUS:38749122092

SN - 0022-247X

VL - 341

SP - 640

EP - 648

JO - Journal of Mathematical Analysis and Applications

JF - Journal of Mathematical Analysis and Applications

IS - 1

ER -

Unitary equivalence to a complex symmetric matrix: An algorithm

Abstract

Access to Document

Other files and links

Cite this