Joint zero sets and ranges of several Hermitian forms over complex and quaternionic scalars

P. Binding, A. Markus

Research output: Contribution to journalArticlepeer-review

2 Scopus citations

Abstract

Let hj:V→ ℝ, j=1,...,n, be Hermitian forms on a inner product space over double-struck F sign=ℂ or ℍ, and let h:V→ ℝn have jth component hj. We study path connectedness of the joint zero set h-1(0)∩V1 and convexity of the joint range h(V1) for various values of n, where V1 is the unit sphere of V.

Original languageEnglish
Pages (from-to)63-72
Number of pages10
JournalLinear Algebra and Its Applications
Volume385
Issue number1-3
DOIs
StatePublished - 1 Jul 2004

Keywords

  • Hausdorff-Toeplitz theorem
  • Hermitian form
  • Joint range
  • Joint zero set
  • Quaternionic inner product space

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