Numerical range of a normal compression

Hwa Long Gau, Pei Yuan Wu

Research output: Contribution to journalArticlepeer-review

12 Scopus citations

Abstract

Let N be an n-by-n diagonal matrix whose distinct eigenvalues form corners of their convex hull, let x be a vector in ℂn with nonzero components, and let A be the compression of N to the orthogonal complement of x. In this article, we study the properties of the eigenvalues and the numerical range of A and show that in many ways they are analogous to the ones for unitary N. The approach via the diagonal form of N yields a much simpler proof for some of the main results in this area.

Original languageEnglish
Pages (from-to)195-201
Number of pages7
JournalLinear and Multilinear Algebra
Volume52
Issue number3-4
DOIs
StatePublished - 2004

Keywords

  • Normal compression
  • Numerical range

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