A faster algorithm for identification of an M-Matrix

M-matrices are important in the consideration of rates of convergence of iterative methods for solving large systems of equations and are applicable in areas such as input-output systems in economic modelling, queuing theory, and engineering. The usual definition of an M-matrix has, among other requirements, that it must be non-singular and its inverse non-negative. Following Saad (2003), Young (1971) and Berman and Shaked--Monderer (2003) two more easily checked characterisations of an M-matrix are explored. These require only the evaluation of the spectral radius of an associated non-negative matrix.