@article{7fc12923250f4ed5ae355582864d6577,
title = "ON LOW-DIMENSIONAL PARTIAL ISOMETRIES",
abstract = "Two statements concerning n-by-n partial isometries are being considered: (i) these matrices are generic, if unitarily irreducible, and (ii) if nilpotent, their numerical ranges are circular disks. Both statements hold for n ≤ 4 but fail starting with n = 5.",
keywords = "Kippenhahn polynomial, Numerical range, Partial isometry",
author = "Qixiao He and Spitkovsky, {Ilya M.} and Ibrahim Suleiman",
note = "Funding Information: †Division of Science and Mathematics, New York University Abu Dhabi (NYUAD), Saadiyat Island, P.O. Box 129188 Abu Dhabi, United Arab Emirates. The results are partially based on the Capstone projects of [QH] (2019-20) and [IS] (2021-22 academic year) under the supervision of [IMS]. The latter was also supported in part by Faculty Research funding from the Division of Science and Mathematics, New York University Abu Dhabi (imspitkovsky@gmail.com). Publisher Copyright: {\textcopyright} 2023, International Linear Algebra Society. All rights reserved.",
year = "2023",
doi = "10.13001/ela.2023.7405",
language = "English (US)",
volume = "39",
pages = "124--135",
journal = "Electronic Journal of Linear Algebra",
issn = "1537-9582",
publisher = "International Linear Algebra Society",
}