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

2020/11/26 by Mackenzie Cox, Cox, Mackenzie, Weston M. Grewe +7
Computer Science · Mathematics · #15A60 #47A12 #Advanced Topics in Algebra #Algebraic and Geometric Analysis #FOS: Mathematics #Functional Analysis (math.FA) #Matrix Theory and Algorithms

paper · pdf · doi:10.48550/arxiv.2011.13409

openalex publication_date 2020/11/26 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

The 4-by-4 nilpotent matrices the numerical ranges of which have non-parallel\nflat portions on their boundary that are on lines equidistant from the origin\nare characterized. Their numerical ranges are always symmetric about a line\nthrough the origin and all possible angles between the lines containing the\nflat portions are attained.\n

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