@inbook{14a47a320c67420f8d202c4de5eba59c,
title = "Numerical ranges of 4-By-4 nilpotent matrices: Flat portions on the boundary",
abstract = "In their 2008 paper Gau and Wu conjectured that the numerical range of a 4-by-4 nilpotent matrix has at most two flat portions on its boundary. We prove this conjecture, establishing along the way some additional facts of independent interest. In particular, a full description of the case in which these two portions indeed materialize and are parallel to each other is included.",
keywords = "Nilpotent matrix, Numerical range",
author = "Erin Militzer and Patton, {Linda J.} and Spitkovsky, {Ilya M.} and Tsai, {Ming Cheng}",
year = "2017",
doi = "10.1007/978-3-319-49182-0_23",
language = "English (US)",
series = "Operator Theory: Advances and Applications",
publisher = "Springer International Publishing",
pages = "561--591",
booktitle = "Operator Theory",
}