Let A be a real symmetric positive definite matrix. Show that |aij|<(aii+ajj)/2 for i not equal to j.
The Attempt at a Solution
I really don't even know where to start with this. I think that aii and ajj 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??