Open AccessNonparallel flat portions on the boundaries of numerical ranges of 4-by-4 nilpotent matrices
Author(s) -
Mackenzie Cox,
Weston M. Grewe,
Grace K. Hochrein,
Linda J. Patton,
Ilya M. Spitkovsky
Publication year - 2021
Publication title -
the electronic journal of linear algebra
Language(s) - English
Resource type - Journals
eISSN - 1537-9582
pISSN - 1081-3810
DOI - 10.13001/ela.2021.5785
Subject(s) - equidistant , mathematics , nilpotent , boundary (topology) , line (geometry) , geometry , nilpotent matrix , mathematical analysis , numerical analysis , pure mathematics , eigenvalues and eigenvectors , symmetric matrix , physics , matrix function , quantum mechanics
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.