Abstract
We consider the class of doubly diagonally dominant matrices ( A = [a ij ] ϵ C n, n , ∥a ii ||a jj ∥ ⩾ ∑ k ≠ i |a ik |∑ k ⩞ j |a jk |, i ≠ j ) and its subclasses. We give necessary and sufficient conditions in terms of the directed graph for an irreducibly doubly diagonally dominant matrix to be a singular matrix or to be an H -matrix. As in the case of diagonal dominance, we show that the Schur complements of doubly diagonally dominant matrices inherit this property. Moreover, we describe when a Schur complement of a strictly doubly diagonally dominant matrix is strictly diagonally dominant.
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