- Aide Scilab
- Algèbre Lineaire
- bdiag
- chfact
- chol
- chsolve
- cmb_lin
- coff
- colcomp
- companion
- cond
- det
- expm
- fullrf
- fullrfk
- givens
- glever
- gspec
- hess
- householder
- inv
- kernel
- linsolve
- lu
- lyap
- nlev
- orth
- pbig
- pinv
- polar
- proj
- qr
- range
- rank
- rcond
- rowcomp
- spec
- sqroot
- squeeze
- sva
- svd
- trace
- aff2ab
- balanc
- classmarkov
- eigenmarkov
- ereduc
- fstair
- genmarkov
- gschur
- im_inv
- kroneck
- lsq
- pencan
- penlaur
- projspec
- psmall
- quaskro
- randpencil
- rankqr
- rowshuff
- rref
- schur
- spaninter
- spanplus
- spantwo
- sylv
Please note that the recommended version of Scilab is 2024.1.0. This page might be outdated.
See the recommended documentation of this function
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
<< classmarkov | Algèbre Lineaire | ereduc >> |