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If $A=(a_{ij})$ is positive semidefinite, prove that $a_{ij}^2 \leq a_{ii}a_{jj}$ for all $i \neq j$.
I don't even know how to get started, any hint is appreciated, thanks a lot.

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    see related http://math.stackexchange.com/questions/235170/necessary-condition-for-positive-semidefiniteness-is-it-sufficient/235224#2352242012-11-20

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