The product field of values

Daniel Corey, Charles R. Johnson, Ryan Kirk, Brian Lins, Ilya Spitkovsky

Research output: Contribution to journalArticlepeer-review


For two n-by-n matrices, A,B, the product field of values is the set P(A,B)={〈Ax,x〉〈Bx,x〉:x∈Cn,||x||=1}. In this paper, we establish basic properties of the product field of values. The main results are a proof that the product field is a simply connected subset of the complex plane and a characterization of matrix pairs for which the product field has nonempty interior.

Original languageEnglish (US)
Pages (from-to)2155-2173
Number of pages19
JournalLinear Algebra and Its Applications
Issue number5
StatePublished - Mar 1 2013


  • Field of values
  • Numerical range

ASJC Scopus subject areas

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


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