Re: General 3-state stochastic matrix (again)

*To*: mathgroup at smc.vnet.net*Subject*: [mg58233] Re: General 3-state stochastic matrix (again)*From*: Virgil Stokes <virgil.stokes at neuro.ki.se>*Date*: Fri, 24 Jun 2005 02:49:51 -0400 (EDT)*References*: <200506230929.FAA16127@smc.vnet.net>*Sender*: owner-wri-mathgroup at wolfram.com

Steven M. Christensen wrote: > Your email has come to me with a lot of non-ascii symbols. > >Please resend this in pure ascii so we can understand what it >is. > >Moderator > > > > >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: > > > >Clear[\116\0612, \116\0613, \116\0621, \116\0623, \116\0631, \116\0632] >T = {{1 - \116\0612 - \116\0613, \116\0612, \116\0613}, {\116\0621, 1 - \116\0621 - \116\0623, \116\0623}, {\116\0631, \116\0632, 1 - \116\0631 - \116\0632}}; >MatrixForm[T] >xx = MatrixPower[T, n]; > >MatrixForm[%] >TimeUsed[] >zz = Limit[xx, n -> \142\010\036, Assumptions -> 0 < \116\0612 < 1 && >0 < \116\0613 < 1 && 0 < \116\0612 + \116\0613 < 1 && 0 < \116\0621 < 1 && > 0 < \116\0623 < 1 && 0 < \116\0621 + \116\0623 < 1 && 0 < \116\0631 < 1 >&& 0 < \116\0632 < 1 && 0 < >\116\0631 + \116\0632 < 1] // FullSimplify; >TimeUsed[] >MatrixForm[zz] > >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. > >Note, for a general 2-state stochastic matrix, the above approach works >fine. > >--Thanks, >V. Stokes > > > > > > > > [Anybody want to indicate how to avoid the symbols in an email above - moderator] I have tried several different copy types from Mathematica and finally used one that when I sent it to myself looked fine. So on my system Win2K with Mathematica 5.1 it looks fine in the email that I sent to myself before posting it to the Mathematica group. What do you suggest that I do? --V. Stokes