Numerical Ranges of 4-by-4 Nilpotent Matrices: Flat Portions on the Boundary

Erin Militzer, Linda J. Patton, Ilya M. Spitkovsky +1

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, establishi…