Re: General 3-state stochastic matrix

*To*: mathgroup at smc.vnet.net*Subject*: [mg58251] Re: General 3-state stochastic matrix*From*: Paul Abbott <paul at physics.uwa.edu.au>*Date*: Fri, 24 Jun 2005 03:28:41 -0400 (EDT)*Organization*: The University of Western Australia*References*: <d98p16$eeo$1@smc.vnet.net>*Sender*: owner-wri-mathgroup at wolfram.com

In article <d98p16$eeo$1 at smc.vnet.net>, Virgil Stokes <virgil.stokes at it.uu.se> wrote: > I have tried to find the limit (as n, the power of the matrix, goes to > infinity) for the general 3-state stochastic matrix using the following > code: It was very difficult to read this posting due to the weird fonts. > However, it does not find a symbolic solution. I would appreciate it > greatly if someone else could look at this and see if they are able to > get a symbolic solution. Warning! this can take considerable CPU time. Instead of computing the power of a matrix using MatrixPower and then taking the limit, a better approach is to diagonalize the matrix first, so that computing the power becomes trivial. Also, since the maximal eigenvalue of a stochastic matrix is unity, all entries in this diagonal matrix vanish, except for the one corresponding to unit eigenvalue. The Notebook http://physics.uwa.edu.au/pub/Mathematica/MathGroup/StochasticMatrices.nb shows how to obtain the steady state matrix for an n-state stochastic matrix. Cheers, Paul -- Paul Abbott Phone: +61 8 6488 2734 School of Physics, M013 Fax: +61 8 6488 1014 The University of Western Australia (CRICOS Provider No 00126G) AUSTRALIA http://physics.uwa.edu.au/~paul http://InternationalMathematicaSymposium.org/IMS2005/