The product field of values

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

Research output: Contribution to journalArticle

Abstract

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
Volume438
Issue number5
DOIs
StatePublished - Mar 1 2013

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Field of Values
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Keywords

  • Field of values
  • Numerical range

ASJC Scopus subject areas

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

Cite this

The product field of values. / Corey, Daniel; Johnson, Charles R.; Kirk, Ryan; Lins, Brian; Spitkovsky, Ilya.

In: Linear Algebra and Its Applications, Vol. 438, No. 5, 01.03.2013, p. 2155-2173.

Research output: Contribution to journalArticle

Corey, D, Johnson, CR, Kirk, R, Lins, B & Spitkovsky, I 2013, 'The product field of values', Linear Algebra and Its Applications, vol. 438, no. 5, pp. 2155-2173. https://doi.org/10.1016/j.laa.2012.09.028
Corey, Daniel ; Johnson, Charles R. ; Kirk, Ryan ; Lins, Brian ; Spitkovsky, Ilya. / The product field of values. In: Linear Algebra and Its Applications. 2013 ; Vol. 438, No. 5. pp. 2155-2173.
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