Group generalized inverses of M-matrices associated with periodic and nonperiodic jacobi matrices

Abstract

We consider two types of irreducible stochastic matrices —tridiagonal matrices and periodic jacobi matrices —which can be viewed as transition matrices of interval and circular random walks,respcetively. For both types of matrices we give a formula for the group inverse of the associated singular M-matrix. We discuss both the sign patterns and the relative sizes of the entries in these group inverses and apply our results to give qualitative information about random walks on an interval and on a circle.