The Generalized Numerical Range of a Set of Matrices

Pan Shun Lau, Chi Kwong Li, Yiu Tung Poon, Nung Sing Sze

Research output: Journal article publicationJournal articleAcademic researchpeer-review

1 Citation (Scopus)


For a given set of n×n matrices F, we study the union of the C-numerical ranges of the matrices in the set F, denoted by WC(F). We obtain basic algebraic and topological properties of WC(F), and show that there are connections between the geometric properties of WC(F) and the algebraic properties of C and the matrices in F. Furthermore, we consider the starshapedness and convexity of the set WC(F). In particular, we show that if F is the convex hull of two matrices such that WC(A) and WC(B) are convex, then the set WC(F) is star-shaped. We also investigate the extensions of the results to the joint C-numerical range of an m-tuple of matrices.

Original languageEnglish
Pages (from-to)24-46
Number of pages23
JournalLinear Algebra and Its Applications
Publication statusPublished - 15 Feb 2019


  • Convex set
  • Numerical range
  • Star-shaped set

ASJC Scopus subject areas

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


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