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## Homework Statement

In a symmetric positive definite matrix, why does max{|a

_{ij}|}=max{|a

_{ii}|}

## Homework Equations

|a

_{ij}|≤(a

_{ii}+a

_{jj})/2

## The Attempt at a Solution

max{|a

_{ij}|}≤max{(a

_{ii}+a

_{jj})/2

max{|a

_{ij}|}≤max{a

_{ii}/2}+max{a

_{jj}/2}

max{|a

_{ij}|}≤[itex]\frac{1}{2}[/itex]max{a

_{ii}}+[itex]\frac{1}{2}[/itex]max{a

_{jj}}

then I am stuck! :(