Let P be a stochastic matrix. Then: (a) P is similar to a matrix of the form Ik O where 1 & X(K). (b) If the Markov chain (of which P is the transition matrix) is ergodic then k = 1, i.e., P is similar to [B] where 1 A(K). where p(K) < 1. " (c) If the chain is regular, lim Kn = 0. 818 (d) If the chain is absorbing, with r absorbing states, then P can be written, by rearranging states, as follows P- [1 2] = RK >