Abstract
ABSTRACT We give a computational criterion for the boundary points of the higher rank numerical range of a matrix and describe a general scheme for constructing its boundary curve. The results are used to study the diameter and minimal width of the higher rank numerical range. A detailed study on a 6-by-6 matrix is done. While its rank-2-numerical range is not of constant width, it shares interesting properties similar to convex sets with constant width. A conjecture on the classical numerical range is extended to the higher rank numerical range, namely, the higher rank numerical range of a matrix has constant width if and only if it is a circular disk.
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