Why does the definition of Diagonally Dominant matrices consider the sums in the row, not in the columns? So diagonally dominant matrices are defined to be matrices such that on each row, the absolute value of the diagonal element is larger than the sum of the absolute values of the other elements. Why is it defined this way? Why the sum of row elements, and not column elements?

I think it is just a convention.

If we look at the wikipedia page.

> The definition in the first paragraph sums entries across rows. It is therefore sometimes called row diagonal dominance. If one changes the definition to sum down columns, this is called column diagonal dominance.