Nonparallel flat portions on the boundaries of numerical ranges of 4-by-4 nilpotent matrices
Mackenzie Cox, Weston Grewe, Grace K. Hochrein, Linda J. Patton, Ilya M. Spitkovsky · Electronic Journal of Linear Algebra · 2021
The 4-by-4 nilpotent matrices whose numerical ranges have nonparallel flat portions on their boundary that are on lines equidistant from the origin are characterized. Their numerical ranges are always symmetric about a line through the origin and all possible angles between the lines containing the flat portions are attained.