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Re: How to solve matrix equitions -- LinearSolve?

  • To: mathgroup at smc.vnet.net
  • Subject: [mg22416] Re: [mg22187] How to solve matrix equitions -- LinearSolve?
  • From: Rob Pratt <rpratt at email.unc.edu>
  • Date: Wed, 1 Mar 2000 00:40:10 -0500 (EST)
  • Sender: owner-wri-mathgroup at wolfram.com

Your system is overdetermined (n+1 equations but only n unknowns), so
arbitrarily remove the last equation of PI = PI . Q, replacing it with
the normalizing equation.

LinearSolve[
    ReplacePart[Transpose[IdentityMatrix[Length[Q]] - Q], 
	Table[1, {Length[Q]}], -1], 
    Join[Table[0., {Length[Q]-1}], {1}]]

I have done many such computations in analyzing the board game
Monopoly as a Markov process.  See my site below.

Rob Pratt
Department of Operations Research
The University of North Carolina at Chapel Hill

rpratt at email.unc.edu

http://www.unc.edu/~rpratt/

On Thu, 17 Feb 2000, Wang, Xiaoguang(Freeman) wrote:

> Hi,
> 
> I want to solve such equations about Markov Chain
> 
> Vector : PI 1xn
> Matrix : Q nxn
> 
> PI  = PI . Q and
> Sum(PI0, PI1, .. PIn) = 1
> 
> How could I solve this problem in Mathematica? Which command should I use?
> 
> Thanks.
> Xiaoguang



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