Necessary and sufficient conditions for a matrix to be causative in a nonstationary Markov chain

AbstractGiven a sequence of transition matrices for a nonstationary Markov chain, a matrix whose product on the right of a transition matrix yields the next transition matrix is called a causative matrix. A causative matrix is strongly causative if successive products continue to yield stochastic matrices. This paper presents necessary and sufficient conditions for a matrix to be causative and strongly causative with respect to an invertible transition matrix, by considering the causative matrix as a linear transformation on the rows of the transition matrix