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Does the sin-theta theorem imply a componentwise nonasymptotic bound for eigenvectors? Assume, for the purpose of this question, that the eigenvalues concerned are simple.

If this is trivial, I apologize in advance. I have just landed on eigenspace perturbation planet.

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  • $\begingroup$ What is sintheta ? $\endgroup$
    – Alexander Chervov
    Commented May 9, 2012 at 20:04
  • $\begingroup$ @Felix: Even though this perturbation result that you mention is standard in some contexts, it does not hurt to provide an explicit link or theorem, otherwise the question feels rather incomplete. $\endgroup$
    – Suvrit
    Commented May 9, 2012 at 21:43
  • $\begingroup$ I mean something like this: books.google.ie/… $\endgroup$
    – Felix Goldberg
    Commented May 9, 2012 at 22:50

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