Nonparallel 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

doi:10.13001/ela.2021.5785

Nonparallel 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

Mathematics

Research output: Contribution to journal › Article › peer-review

Abstract

The 4-by-4 nilpotent matrices whose numerical ranges have nonparallel 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.

Original language	English (US)
Pages (from-to)	504-523
Number of pages	20
Journal	Electronic Journal of Linear Algebra
Volume	37
DOIs	https://doi.org/10.13001/ela.2021.5785
State	Published - 2021

Keywords

Nilpotent matrices
Numerical ranges

ASJC Scopus subject areas

Algebra and Number Theory

Access to Document

10.13001/ela.2021.5785

Cite this

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title = "Nonparallel flat portions on the boundaries of numerical ranges of 4-by-4 nilpotent matrices∗",

abstract = "The 4-by-4 nilpotent matrices whose numerical ranges have nonparallel 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.",

keywords = "Nilpotent matrices, Numerical ranges",

author = "Mackenzie Cox and Grewe, {Weston M.} and Hochrein, {Grace K.} and Patton, {Linda J.} and Spitkovsky, {Ilya M.}",

year = "2021",

doi = "10.13001/ela.2021.5785",

language = "English (US)",

volume = "37",

pages = "504--523",

journal = "Electronic Journal of Linear Algebra",

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publisher = "International Linear Algebra Society",

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AU - Cox, Mackenzie

AU - Grewe, Weston M.

AU - Hochrein, Grace K.

AU - Patton, Linda J.

AU - Spitkovsky, Ilya M.

PY - 2021

Y1 - 2021

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AB - The 4-by-4 nilpotent matrices whose numerical ranges have nonparallel 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.

KW - Nilpotent matrices

KW - Numerical ranges

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JF - Electronic Journal of Linear Algebra

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