On some 4-by-4 matrices with bi-elliptical numerical ranges

Titas Geryba, Ilya M. Spitkovsky

Research output: Contribution to journalArticlepeer-review


A complete description of 4-by-4 matrices (Formula presented.), with scalar 2-by-2 diagonal blocks, for which the numerical range is the convex hull of two non-concentric ellipses is given. This result is obtained by reduction to the leading special case in which (Formula presented.) also is a scalar multiple of the identity. In particular cases when in addition (Formula presented.) is real or pure imaginary, the results take an especially simple form. An application to reciprocal matrices is provided.

Original languageEnglish (US)
Pages (from-to)855-870
Number of pages16
JournalLinear and Multilinear Algebra
Issue number5
StatePublished - 2021


  • Numerical range
  • bi-elliptical shape
  • reciprocal matrix

ASJC Scopus subject areas

  • Algebra and Number Theory


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