eigenmarkov

normalized left and right Markov eigenvectors

Calling Sequence

[M,Q]=eigenmarkov(P)

Arguments

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

one.

: :M real matrix with N columns. : :Q real matrix with N rows. :

Description

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).

Examples

//P has two recurrent classes (with 2 and 1 states) 2 transient states
P=`genmarkov`_([2,1],2)
[M,Q]=eigenmarkov(P);
P*Q-Q
Q*M-P^20

See Also

• genmarkov generates random markov matrix with recurrent and transient classes
• classmarkov recurrent and transient classes of Markov matrix