Nonparallel flat portions on the boundaries of numerical ranges of 4-by-4 nilpotent matrices

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Mackenzie Cox
Weston Grewe
Grace Hochrein
Linda Patton
Ilya Spitkovsky

Abstract

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.

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