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arXiv · 2011.13409

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

Mackenzie Cox·Weston M. Grewe·Grace K. Hochrein·Linda J. Patton·Ilya M. Spitkovsky
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Abstract

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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Mackenzie Cox, Weston M. Grewe, Grace K. Hochrein, Linda J. Patton, Ilya M. Spitkovsky. 2020-11-26. Non-parallel Flat Portions on the Boundaries of Numerical Ranges of 4-by-4 Nilpotent Matrices. https://arxiv.org/abs/2011.13409

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