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I'm trying to find the stationary distribution of T, a transition matrix (Markov Chain). After I solve the equations of the matrix, I can't get to their values, does that mean that T doesn't have a stationary distribution?

What is the best way to check if a transition matrix does have a stationary distribution?

0.3 0.0 0.5 0.2
0.0 0.4 0.3 0.3
0.3 0.2 0.0 0.5
0.4 0.1 0.0 0.5
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Finite-state Markov chains always have a stationary distribution, not always unique, though. You find them by finding left eigenvectors for the eigenvalue 1.

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