Numerical ranges of companion matrices: flat portions on the boundary

Jeffrey Eldred, Leiba Rodman, Ilya Spitkovsky

Research output: Contribution to journalArticle


Criterion for a companion matrix to have a certain number of flat portions on the boundary of its numerical range is given. The criterion is specialized to the cases of 3 × 3 and 4 × 4 matrices. In the latter case, it is proved that a 4 × 4 unitarily irreducible companion matrix cannot have three flat portions on the boundary of its numerical range. Numerical examples are given to illustrate the main results.

Original languageEnglish (US)
Pages (from-to)1295-1311
Number of pages17
JournalLinear and Multilinear Algebra
Issue number11-12
Publication statusPublished - Nov 1 2012



  • companion matrix
  • numerical range

ASJC Scopus subject areas

  • Algebra and Number Theory

Cite this