Let $A, B$ be $ntimes n$ positive semidefinite matrices. Bhatia and Kittaneh asked whether it is true $$ sqrt{sigma_j(AB)}le frac{1}{2} lambda_j(A+B), qquad j=1, ldots, n$$ where $sigma_j(cdot)$, $lambda_j(cdot)$, are the $j$-th largest singular value, eigenvalue, respectively. The question was recently solved by Drury in the affirmative. This article revisits Drurys solution. In particular, we simplify the proof for a key auxiliary result in his solution.
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