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.