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Numerical Ranges of 4-by-4 Nilpotent Matrices: Flat Portions on the Boundary by Militzer, Erin; Patton, Linda J.; Spitkovsky, Ilya M.; Tsai, Ming-Cheng is a scholarly article available to read on EtoBox.

What is Numerical Ranges of 4-by-4 Nilpotent Matrices: Flat Portions on the Boundary about?

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.

Author

Militzer, Erin; Patton, Linda J.; Spitkovsky, Ilya M.; Tsai, Ming-Cheng

Published

2015

Language

EN