componentwise eigenvector perturbation

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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What is sintheta ? –  Alexander Chervov May 9 '12 at 20:04
@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. –  Suvrit May 9 '12 at 21:43
I mean something like this: books.google.ie/… –  Felix Goldberg May 9 '12 at 22:50