On the condition of nearly singular matrices under rank-1 perturbations

Tony F. Chan*, Diana C. Resasco

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

1 Scopus citations


Let A be an n-by-n nearly singular matrix with Rank(A)≥n - 1 and singular values d1≥⋯≥dn-1 > dn, where dn can be small or zero. Consider the rank-1 modification of A: A ̂=A+αzwT, with {norm of matrix}z{norm of matrix} = {norm of matrix}w{norm of matrix} = 1. We give lower and upper bounds for the condition number of  in terms of |α| and the angles between z and w and the singular vectors of A corresponding to dn.

Original languageEnglish (US)
Pages (from-to)223-232
Number of pages10
JournalLinear Algebra and Its Applications
Issue numberC
StatePublished - Apr 1986
Externally publishedYes

ASJC Scopus subject areas

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


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