Preservers of eigenvalue inclusion sets of matrix products

Virginia Forstall, Aaron Herman, Chi Kwong Li, Nung Sing Sze, Vincent Yannello

Research output: Journal article publicationJournal articleAcademic researchpeer-review

4 Citations (Scopus)

Abstract

For a square matrix A, let S(A) be an eigenvalue inclusion set such as the Gershgorin region, the union of Cassini ovals, and the Ostrowski's set. Characterization is obtained for maps Φ on n×n matrices satisfying S(Φ(A)Φ(B))=S(AB) for all matrices A and B.
Original languageEnglish
Pages (from-to)285-293
Number of pages9
JournalLinear Algebra and Its Applications
Volume434
Issue number1
DOIs
Publication statusPublished - 1 Jan 2011

Keywords

  • Brauer's set
  • Cassini ovals
  • Gershgorin regions
  • Ostrowski set
  • Preservers

ASJC Scopus subject areas

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

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