We give an account of some results, both old and new, about any $n\times n$ Markov matrix that is embeddable in a one-parameter Markov semigroup. These include the fact that its eigenvalues must lie in a certain region in the unit ball. We prove that a well-known procedure for approximating a non-embeddable Markov matrix by an embeddable one is optimal in a certain sense.
"Embeddable Markov Matrices." Electron. J. Probab. 15 1474 - 1486, 2010. https://doi.org/10.1214/EJP.v15-733