Non-parallel Flat Portions on the Boundaries of Numerical Ranges of 4-by-4 Nilpotent Matrices
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 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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