I have a transition matrix of
and calculated eigenvalues of :
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?