ELA, Volume 13, pp. 162-174, July 2005, abstract.

Subdirect Sums of Nonsingular M-matrices and 
of their Inverses 

Rafael Bru, Francisco Pedroche, and 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.