On matrices with elliptical numerical ranges

Ethan S. Brown, Ilya M. Spitkovsky

Research output: Contribution to journalArticlepeer-review


It is known that for several classes of matrices, including quadratic and certain tridiagonal matrices, the numerical range is an ellipse. We prove this result for a larger class of matrices, encompassing these published results as well as providing other sufficient conditions for ellipticity. The proof gives an explanation for this phenomenon and, in certain cases, provides an explicit description of the numerical range.

Original languageEnglish (US)
Pages (from-to)177-193
Number of pages17
JournalLinear and Multilinear Algebra
Issue number3-4
StatePublished - 2004


  • Numerical range
  • Tridiagonal matrices

ASJC Scopus subject areas

  • Algebra and Number Theory


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