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.
CITATION STYLE
Militzer, E., Patton, L. J., Spitkovsky, I. M., & Tsai, M. C. (2017). Numerical ranges of 4-By-4 nilpotent matrices: Flat portions on the boundary. In Operator Theory: Advances and Applications (Vol. 259, pp. 561–591). Springer International Publishing. https://doi.org/10.1007/978-3-319-49182-0_23
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