# Result on Strict diagonally dominant matrix

Given a strictly diagonally dominant matrix $A$ i.e., $|a_{ii}| > \sum_{j=1,i \neq j}^{n} |a_{ij}|$ for $i = 1 \cdots n$. I need to show that there is atleast one column k which is dominant i.e to show $|a_{kk}| > \sum_{j=1,k \neq j}^{n} |a_{jk}|$ for at least one value of $k = 1 \cdots n$

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What if it isn't for any $k$? –  scineram Nov 3 '11 at 6:48