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I have a transition matrix of

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and calculated eigenvalues of :

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How can I calculate the eigenvector and general probability distribution

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Defining e as the vector that contains the eigenvalues, and v as the eigenvector, this should hold: Tv = ev. You can write this out and obtain a system of equations which you can solve. It results in the following; v1 = v2 and v2 = -v3. So take v1 = 1 and your eigenvector will be: v = (1 1 -1)

By the general probability distribution, do you mean the long run probabilities?

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  • $\begingroup$ Yes what would that be ? $\endgroup$ – user3443632 Jan 14 '16 at 14:11
  • $\begingroup$ Then you have to solve: pi*T = pi, where pi is the long-run probability vector. Try yourself. $\endgroup$ – pk_22 Jan 14 '16 at 14:34

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