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