Characterization of diagonally dominant H-matrices

Abstract

We show that the diagonal dominance nonsingularity result of Shivakumar and Chew from 1974, and the diagonal dominance nonsingularity result of Farid from 1995, and the result of Huang on characterization of diagonally dominant H-matrices from 1995, all proven independently and in different contexts are, in fact, equivalent. We also offer the fourth and the fifth simpler equivalent conditions, for a diagonally dominant matrix to be an H-matrix.