How can we find transition matrix for given stationary distribution e.g [1/4, 2/4, 1/4]. I know the sum of each row equals 1, from $A*v=v$, we can get 3 more equations and the last 3 from property $\pi_i*q_{ij} = \pi_j*q_{ji}$. Honestly, it seems an overkill, to do it all of it. Is there a faster way?
How it is solved in bigger matrices?
I read that Metropolis-Hastings could be used, but I could not find an example for this particular problem.