Variational principles for indefinite eigenvalue problems

Paul Binding, Qiang Ye

Research output: Contribution to journalArticlepeer-review

12 Scopus citations


Let A and B be N × N complex Hermitian matrices where B is nonsingular but neither A nor B need be definite. Let Sk denote the linear subspaces of CN of codimension k, and let σ±k = sup{inf{x∗ Ax : x∗ Bx = ±1, x ∈ S} : S ∈ Sk−1}. Assuming that the real eigenvalues λ of the problem Aχ = λBχ are semisimple, we show how to calculate the value of each σ±k and the corresponding inf sups. In consequence we show precisely which eigenvalues of (∗) can be obtained by variational formulae of the above types.

Original languageEnglish
Pages (from-to)251-262
Number of pages12
JournalLinear Algebra and Its Applications
StatePublished - 1995

ASJC Scopus subject areas

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


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