How well-conditioned can the eigenvalue problem be?

Carlos Beltrán, Laurent Bétermin, Peter Grabner, Stefan Steinerberger

Research output: Contribution to journalArticlepeer-review


The condition number for eigenvalue computations is a well--studied quantity. But how small can we expect it to be? Namely, which is a perfectly conditioned matrix w.r.t. eigenvalue computations? In this note we answer this question with exact first order asymptotic.
Original languageEnglish
JournalMathematics of Computation
Publication statusE-pub ahead of print - 17 May 2021


  • math.NA
  • cs.NA
  • math.CA
  • 65F15 (Primary), 31C20 (Secondary)


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