Subdirect sums of nonsingular M-matrices and of their inverses

Abstract

The question of when the subdirect sum of two nonsingular M -matrices is a nonsingular M -matrix is studied. Sufficient conditions are given. The case of inverses of M -matrices is
also studied. In particular, it is shown that the subdirect sum of overlapping principal submatrices
of a nonsingular M -matrix is a nonsingular M -matrix. Some examples illustrating the conditions
presented are also given.