Subdirect sums of nonsingular M-matrices and of their inverses

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Rafael Bru
Francisco Pedroche
Daniel B. Szyld


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.

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