When is the numerical range of a nilpotent matrix circular?

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Abstract

The problem formulated in the title is investigated. The case of nilpotent matrices of size at most 4 allows a unitary treatment. The numerical range of a nilpotent matrix M of size at most 4 is circular if and only if the traces trM* M2 and trM* M3 are null. The situation becomes more complicated as soon as the size is 5. The conditions under which a 5 × 5 nilpotent matrix has circular numerical range are thoroughly discussed.

Original languageEnglish (US)
Pages (from-to)269-275
Number of pages7
JournalApplied Mathematics and Computation
Volume216
Issue number1
DOIs
Publication statusPublished - Mar 1 2010

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Keywords

  • Nilpotent matrix
  • Numerical range
  • Primary 15A60
  • Secondary 47A12

ASJC Scopus subject areas

  • Computational Mathematics
  • Applied Mathematics

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