Scilab Website | Contribute with GitLab | Mailing list archives | ATOMS toolboxes
Scilab Online Help
6.1.0 - Français

Change language to:
English - 日本語 - Português - Русский

Please note that the recommended version of Scilab is 2025.0.0. This page might be outdated.
See the recommended documentation of this function

Aide de Scilab >> Algèbre Lineaire > Matrices de Markov > eigenmarkov

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
Report an issue
<< classmarkov Matrices de Markov genmarkov >>

Copyright (c) 2022-2024 (Dassault Systèmes)
Copyright (c) 2017-2022 (ESI Group)
Copyright (c) 2011-2017 (Scilab Enterprises)
Copyright (c) 1989-2012 (INRIA)
Copyright (c) 1989-2007 (ENPC)
with contributors
Last updated:
Tue Feb 25 08:50:20 CET 2020