Uniqueness problem on numerical ranges of 3-by-3 companion matrices

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Abstract

Abstract For any two 3-by-3 companion matrices A and B with identical numerical ranges, we give a necessary and sufficient condition for A=B in terms of the shapes of numerical ranges and the locations of eigenvalues. In addition, all distinct 3-by-3 companion matrices with identical numerical ranges can be obtained precisely.

Original languageEnglish
Article number13216
Pages (from-to)84-100
Number of pages17
JournalLinear Algebra and Its Applications
Volume482
DOIs
StatePublished - 1 Oct 2015

Keywords

  • Companion matrix
  • Numerical range
  • Uniqueness

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