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Let $A$ be a rank 1 positive semidefinite matrix and $B$ a Hermitian matrix. Suppose I know the eigenvectors of both $A$ and $B$ and that $A-B$ is also positive semidefinite.

Apart from Weyl's inequality is there anything that can be deduced about the eigenvalues of $B$?

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    Not completely sure what you are asking for, since you say you know that eigenvalues of $B$, and that you want to know about the eigenvalues of $B$.2012-12-21
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    Sorry, maybe I've not been clear enough. I know the _eigenvectors_ of $B$ not the eigenvalues. I also know the matrix A since it's rank 1 and I know the eigenvector.2012-12-21
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    My bad, I misread the question.2012-12-21

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