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Necessary and sufficient conditions for a matrix to be causative in a nonstationary Markov chain |
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| Authors: | John Hennessey Barry V. Bye |
| Affiliation: | Loyola College, 4501 North Charles Street, Baltimore, MD, 21210, U.S.A.;Office of Research and Statistics, Social Security Administration, Baltimore, MD, 21235, U.S.A. |
| Abstract: | Given 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. |
| Keywords: | Linear transformation characteristic values characteristic vectors characteristic subspaces systems of linear inequalities causative matrix primary decomposition theorem constant causative matrix chain |
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