# An open set of 4×4 embeddable matrices whose principal logarithm is not a Markov generator

@article{Casanellas2020AnOS, title={An open set of 4×4 embeddable matrices whose principal logarithm is not a Markov generator}, author={Marta Casanellas and Jes'us Fern'andez-S'anchez and Jordi Roca-Lacostena}, journal={Linear and Multilinear Algebra}, year={2020} }

A Markov matrix is embeddable if it can represent a homogeneous continuous-time Markov process. It is well known that if a Markov matrix has real and pairwise-different eigenvalues, then the embeddability can be determined by checking whether its principal logarithm is a rate matrix or not. The same holds for Markov matrices close enough to the identity matrix or that rule a Markov process subjected to certain restrictions. In this paper we prove that this criterion cannot be generalized and we…

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