Stationary distributions and mean first passage times in Markov chains using generalized inverses

The determination of the mean first passage times in finite irreducible discrete time Markov chains requires the computation of a generalized inverse of I-P, where P is the transition matrix of the Markov chain, and also knowledge of the stationary distribution of the Markov chain. Generalized inverses can be used to find stationary distributions. The linking of these two procedures and the computation of stationary distributions using various multi-condition generalized inverses is investigated.