A new proof of a theorem on M-matrices Original Research Article

We provide a new and simpler proof of the following result by J.P. Milaszewicz and L.P. Moledo [Linear Algebra Appl. 195 (1993) 1]. Consider the equation Ax=y, with A a non-singular M-matrix. Suppose that yK≠0 for each nucleus K, and that xi>0 whenever yi<0. Then x has only positive coordinates. The same method is used to prove their results on bounds for the solutions. Moreover, the conditions are weakened.