Diagonally dominant matrix

Summary

A square matrix is diagonally dominant when each row has a large diagonal entry. In absolute value, it is at least the sum of the absolute values of the other entries of its row. It is strictly diagonally dominant when this inequality is strict in every row. A strictly diagonally dominant matrix is invertible, by the Levy–Desplanques theorem. For strictly diagonally dominant matrices, Gaussian elimination needs no pivoting, and the Jacobi and Gauss–Seidel iterations converge.