Elliptic numerical ranges of 4 × 4 matrices

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Let A be an n × n (complex) matrix. Recall that the numerical range W (A) of A is the set {〈Ax, x〉: x ∈ ℂn, ||x|| = 1} in the plane, where 〈·, ·) denotes the usual inner product in ℂn. In this paper a series of tests is given, allowing one to determine when the numerical range of a 4 × 4 matrix A is an elliptic disc.

Original languageEnglish
Pages (from-to)117-128
Number of pages12
JournalTaiwanese Journal of Mathematics
Issue number1
StatePublished - Jan 2006


  • Kippenhahn curve
  • Numerical range


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