Question

Ch diagonal entry is greater than the sum of the absolute values of all other entries in the corresponding row/column.

Answer 1

In mathematics, a square matrix is said to be diagonally dominant if for every row of the matrix, the magnitude of the diagonal entry in a row is larger than or equal to the sum of the magnitudes of all the other (non-diagonal) entries in that row. More precisely, the matrix A is diagonally dominant if

For example, The matrix

is diagonally dominant because

|a11| ≥ |a12| + |a13| since |+3| ≥ |-2| + |+1|

|a22| ≥ |a21| + |a23| since |-3| ≥ |+1| + |+2|

|a33| ≥ |a31| + |a32| since |+4| ≥ |-1| + |+2|