The numerical range of 3 X 3 matrices

Dennis S. Keeler, Leiba Rodman, Ilya M. Spitkovsky

Research output: Contribution to journalArticlepeer-review


Let A be an n X n complex matrix. Then the numerical range of A, W(A), is defined to be {x*Ax : x ∈ ℂn, x*x = 1}. In this article a series of tests is given, allowing one to determine the shape of W( A) for 3 X 3 matrices. Reconstruction of A, up to unitary similarity, from W(A) is also examined.

Original languageEnglish (US)
Pages (from-to)115-139
Number of pages25
JournalLinear Algebra and Its Applications
Issue number1-3
StatePublished - Feb 1997

ASJC Scopus subject areas

  • Algebra and Number Theory
  • Numerical Analysis
  • Geometry and Topology
  • Discrete Mathematics and Combinatorics


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