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# eigenmarkov

normalized left and right Markov eigenvectors

### Syntax

[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

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