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## Homework Statement

Let A be a real symmetric positive definite matrix. Show that |a

_{ij}|<(a

_{ii}+a

_{jj})/2 for i not equal to j.

## Homework Equations

## The Attempt at a Solution

I really don't even know where to start with this. I think that a

_{ii}and a

_{jj}must both be > 0 since they are on the diagonal and real symmetric positive definite matrices have positive diagonal elements. Other than this, I honestly have NO ideas. Does anyone else??