Mackenzie Cox, Weston M. Grewe, Grace K. Hochrein, Linda J. Patton, Ilya M. Spitkovsky
Published 2020-11-26Version 1
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.
Comments: 22 pages, 4 figures
Crouzeix's conjecture, compressions of shifts, and classes of nilpotent matrices
The spectrum of the product of operators, and the product of their numerical ranges
On low-dimensional partial isometries
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