Bounds for singular values based on the eigenvectors

Nir Cohen, Izchak Lewkowicz

Research output: Contribution to journalArticlepeer-review


For a nondefective matrix A ∈ Cn×n, the known inequalities |λk|/χ \ ̌ σk \ ̌ |λk|χ express a bound on the possible ratio between the kth singular value σk of A and its kth eigenvalue λk, based only on the condition number χ of the associated eigenvector matrix. We obtain and analyse several refinements to this bound.

Original languageEnglish
Pages (from-to)227-248
Number of pages22
JournalLinear Algebra and Its Applications
Issue numberC
StatePublished - 15 Apr 1991
Externally publishedYes

ASJC Scopus subject areas

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


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