How a row change in a stochastic matrix affects the corresponding stochastic eigenvector
Darald J. Hartfiel · Linear and Multilinear Algebra · 1981
Let S be a stochastic matrix having 1 as an eigenvalue of multiplicity one. Without loss of generality, suppose that the stochastic eigenvector belonging to 1 is y with y 1 # 0. This paper then describes the set of all stochastic eigenvectors, belonging to 1, of stochastic matrices differing from S in only the first row. This result is used to identify the long run behaviour of the Markov chains belonging to these stochastic matrices.