Are there any techniques for lower-bounding the angle between eigenvectors of a matrix? Or a lower bound on the related quantity of the condition number of the matrix of eigenvectors? In particular I'm looking for bounds that depend on the difference in the corresponding eigenvalues, with larger angles when the eigenvalues are more separated.
For symmetric matrices (and more generally normal matrices) the angles are of course all right angles. I'm looking for techniques that apply to non-normal matrices.
(The particular class of matrices that I care about is stochastic matrices with trace $n-1$ as described in my previous question http://mathoverflow.net/questions/45126/bounds-on-pk1-pk-for-n-by-n-stochastic-matrix-p-with-trace-n .)