Abstract
Within the set of discrete-time Markov chains, a Markov chain is embeddable in case its transition matrix has at least one root that is a stochastic matrix. The present paper examines the embedding problem for discrete-time Markov chains with three states and with real eigenvalues. Sufficient embedding conditions are proved for diagonalizable transition matrices as well as for non-diagonalizable transition matrices and for all possible configurations regarding the sign of the eigenvalues. The embedding conditions are formulated in terms of the projections and the spectral decomposition of the transition matrix.
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