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normalized left and right Markov eigenvectors





real N x N Markov matrix. Sum of entries in each row should add to one.


real matrix with N columns.


real matrix with N rows.


Returns normalized left and right eigenvectors associated with the eigenvalue 1 of the Markov transition matrix P. If the multiplicity of this eigenvalue is m and P is N x N, M is a m x N matrix and Q a N x m matrix. M(k,:) is the probability distribution vector associated with the kth ergodic set (recurrent class). M(k,x) is zero if x is not in the k-th recurrent class. Q(x,k) is the probability to end in the k-th recurrent class starting from x. If P^k converges for large k (no eigenvalues on the unit circle except 1), then the limit is Q*M (eigenprojection).


//P has two recurrent classes (with 2 and 1 states) 2 transient states

See also

  • genmarkov — generates random markov matrix with recurrent and transient classes
  • classmarkov — recurrent and transient classes of Markov matrix
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Last updated:
Tue Mar 07 09:28:43 CET 2023