  We first show that sufficient conditions for a diagonally dominant matrix to
be a nonsingular one (and also an H-matrix), obtained independently by
Shivakumar and Chew in 1974, and Farid in 1995, are equivalent. Then we
simplify the characterization of diagonally dominant H-matrices obtained by
Huang in 1995, and using it prove that the Shivakumar-Chew-Farid sufficient
condition for a diagonally dominant matrix to be an H-matrix, is also
necessary.
