Some of the things I've learned every day since Oct 10, 2016
47: Invariant Distributions as Eigenvectors
November 26, 2016Posted by on
Since a stationary distribution of a finite Markov chain satisfies , where is the transition matrix of , it can be seen as an eigenvector of eigenvalue under the linear transformation by . Specifically, is the intersection of the eigenspace with the hyperplane formed by the constraint that .
(Here the vector space in question is , where is the number of states in .)