THE GAU-WANG-WU CONJECTURE ON PARTIAL ISOMETRIES HOLDS IN THE 5-BY-5 CASE

Ilya M. Spitkovsky; Ibrahim Suleiman; Elias Wegert

doi:10.13001/ela.2022.6541

THE GAU-WANG-WU CONJECTURE ON PARTIAL ISOMETRIES HOLDS IN THE 5-BY-5 CASE

Ilya M. Spitkovsky, Ibrahim Suleiman, Elias Wegert

Mathematics

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

Abstract

Gau, Wang and Wu in their LAMA'2016 paper conjectured (and proved for n < 4) that an n-by-n partial isometry cannot have a circular numerical range with a non-zero center. We prove that this statement holds for n = 5.

Original language	English (US)
Pages (from-to)	107-113
Number of pages	7
Journal	Electronic Journal of Linear Algebra
Volume	38
DOIs	https://doi.org/10.13001/ela.2022.6541
State	Published - 2022

Keywords

Kippenhahn curve
Kippenhahn polynomial
Numerical range
Partial isometry

ASJC Scopus subject areas

Algebra and Number Theory

Access to Document

10.13001/ela.2022.6541

Cite this

@article{963d406aa665411d9166d59ef1214a1d,

title = "THE GAU-WANG-WU CONJECTURE ON PARTIAL ISOMETRIES HOLDS IN THE 5-BY-5 CASE",

abstract = "Gau, Wang and Wu in their LAMA'2016 paper conjectured (and proved for n < 4) that an n-by-n partial isometry cannot have a circular numerical range with a non-zero center. We prove that this statement holds for n = 5.",

keywords = "Kippenhahn curve, Kippenhahn polynomial, Numerical range, Partial isometry",

author = "Spitkovsky, {Ilya M.} and Ibrahim Suleiman and Elias Wegert",

year = "2022",

doi = "10.13001/ela.2022.6541",

language = "English (US)",

volume = "38",

pages = "107--113",

journal = "Electronic Journal of Linear Algebra",

issn = "1537-9582",

publisher = "International Linear Algebra Society",

}

TY - JOUR

T1 - THE GAU-WANG-WU CONJECTURE ON PARTIAL ISOMETRIES HOLDS IN THE 5-BY-5 CASE

AU - Spitkovsky, Ilya M.

AU - Suleiman, Ibrahim

AU - Wegert, Elias

PY - 2022

Y1 - 2022

N2 - Gau, Wang and Wu in their LAMA'2016 paper conjectured (and proved for n < 4) that an n-by-n partial isometry cannot have a circular numerical range with a non-zero center. We prove that this statement holds for n = 5.

AB - Gau, Wang and Wu in their LAMA'2016 paper conjectured (and proved for n < 4) that an n-by-n partial isometry cannot have a circular numerical range with a non-zero center. We prove that this statement holds for n = 5.

KW - Kippenhahn curve

KW - Kippenhahn polynomial

KW - Numerical range

KW - Partial isometry

UR - http://www.scopus.com/inward/record.url?scp=85131562009&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85131562009&partnerID=8YFLogxK

U2 - 10.13001/ela.2022.6541

DO - 10.13001/ela.2022.6541

M3 - Article

AN - SCOPUS:85131562009

SN - 1537-9582

VL - 38

SP - 107

EP - 113

JO - Electronic Journal of Linear Algebra

JF - Electronic Journal of Linear Algebra

ER -

THE GAU-WANG-WU CONJECTURE ON PARTIAL ISOMETRIES HOLDS IN THE 5-BY-5 CASE

Abstract

Keywords

ASJC Scopus subject areas

Access to Document

Other files and links

Fingerprint

Cite this