Nonnegativity of principal minors of generalized inverses of M-matrices (Q796610)

The result of principal interest established in this paper is that if A is an \(n\times n\) singular irreducible M-matrix, then a large class of generalized inverses of A possesses the property that each of its elements has all its principal minors nonnegative. The class contains both the group and the Moore-Penrose generalized inverses of A. An application of these results is that the fundamental matrix of a continuous (in time) ergodic Markov chain on a finite state space has all its principal minors nonnegative.