@article{169b34f9bbf14d79a672c9772eb9a17e,
title = "On matrices with elliptical numerical ranges",
abstract = "It is known that for several classes of matrices, including quadratic and certain tridiagonal matrices, the numerical range is an ellipse. We prove this result for a larger class of matrices, encompassing these published results as well as providing other sufficient conditions for ellipticity. The proof gives an explanation for this phenomenon and, in certain cases, provides an explicit description of the numerical range.",
keywords = "Numerical range, Tridiagonal matrices",
author = "Brown, {Ethan S.} and Spitkovsky, {Ilya M.}",
note = "Funding Information: This research was conducted during the summer of 2002 at the College of William and Mary{\textquoteright}s research Experience for Undergraduates program and was supported by NSF REU grant DMS-99-87803 and NSF grant DMS-99-88579. The second author was also supported by the Semester Research grant from the College of William and Mary. The authors thank the referee for the valuable comments. The first author would also like to thank Christopher Hillar of the University of California, Berkeley, for his useful discussions during the Research. Copyright: Copyright 2018 Elsevier B.V., All rights reserved.",
year = "2004",
doi = "10.1080/0308108031000112589",
language = "English (US)",
volume = "52",
pages = "177--193",
journal = "Linear and Multilinear Algebra",
issn = "0308-1087",
publisher = "Taylor and Francis Ltd.",
number = "3-4",
}