Numerical range of a normal compression II

Hwa Long Gau, Pei Yuan Wu

Research output: Contribution to journalArticlepeer-review

8 Scopus citations


As in the predecessor [Numerical range of a normal compression, Linear and Multilinear Algebra, in press] of this paper, we consider properties of matrices of the form V*NV, where N=diag(a1,⋯,a n+1) is a diagonal matrix with distinct eigenvalues ajs such that each of them is a corner of the convex hull they generate, and V is an (n+1)-by-n matrix with V*V=In such that any nonzero vector orthogonal to the range space of V has all its components nonzero. We obtain that such a matrix A is determined by its eigenvalues up to unitary equivalence, is irreducible and cyclic, and the boundary of its numerical range is a differentiable curve which contains no line segment. We also consider the condition for the existence of another matrix of the above type which dilates to A such that their numerical ranges share some common points with the boundary of the (n+1)-gon a1⋯an+1.

Original languageEnglish
Pages (from-to)121-136
Number of pages16
JournalLinear Algebra and Its Applications
Issue number1-3
StatePublished - 1 Oct 2004


  • Cyclic matrix
  • Irreducible matrix
  • Normal compression
  • Numerical range


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