Suppose we have two positive definite matrices A and B. Is it correct to claim that all the eigenvalues of A+B are greater or equal to those of A?
Please note that:
1 I need to compare all the eigenvalues and not only the largest ones.
2 A and B are not necessarily diagonal.
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$\begingroup$ The Courant minimax principle will work also: en.wikipedia.org/wiki/Courant_minimax_principle $\endgroup$ Jul 29, 2011 at 5:52

1$\begingroup$ Oh, Terry! You are so kind to answer this one, after your work on A. Horn's conjecture, now TaoKnutson's theorem. $\endgroup$ Jul 29, 2011 at 8:41