@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",
note = "Funding Information: ∗Received by the editors on August 21, 2021. Accepted for publication on January 18, 2022. Handling Editor: Tin-Yau Tam. Corresponding Author: Ilya M. Spitkovsky †Division of Science and Mathematics, New York University Abu Dhabi (NYUAD), Saadiyat Island, P.O. Box 129188 Abu Dhabi, United Arab Emirates (ims2@nyu.edu, is1647@nyu.edu). The results are partially based on the Capstone project of the second named author under the supervision of the first named author. The latter was also supported in part by Faculty Research funding from the Division of Science and Mathematics, New York University Abu Dhabi. ‡Institute of Applied Analysis, TU Bergakademie Freiberg, 09596 Freiberg, Germany (wegert@math.tu-freiberg.de). Publisher Copyright: {\textcopyright} 2022, International Linear Algebra Society. All rights reserved.",
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",
}