2 papers
math.FA2020
Non-parallel Flat Portions on the Boundaries of Numerical Ranges of 4-by-4 Nilpotent Matrices
Mackenzie Cox, Weston M. Grewe, Grace K. Hochrein +2
The 4-by-4 nilpotent matrices the numerical ranges of which have non-parallel flat portions on their boundary that are on lines equidistant from the origin are characterized. Their…
math.FA2015
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…