nth step transition matrices

From: Brad Lukoskie <lubr0401 at stcloudstate.edu>
Date: 2008/04/22 Tue PM 06:49:14 CDT
To: r-help at r-project.org
Subject: [R] nth step transition matrices

The list isn't supposed to be used for homework
problems which I'm pretty certain this is but
#R is difficult at first so i'll show you but you really need to do  
these things on your own or you'll NEVER learn R. I don't want to  
sound like a philosopher but it's really true that learning ,  
particularly in programming, can only be attained by doing.

here's the function and a test case but
make sure you understand what's happening and
keep it hush, hush. I followed Rolf's layout.


matpow<-function(M,n) {

    result<-M

    for ( iter in (2:n)) {
       result<-M%*%result
    }
    return(result)
}

testMat<-matrix(c(.95,0.05,0.01,0.99),nrow=2,byrow=TRUE)
transMat<-matpow(testMat,2)

print(transMat)

Hello,

I have a question in regards to markov chains and transition
probabilities.

I am trying to figure out a way to calculate the "kth-step transition
matrix" of a given matrix.

Say for example I have a single step 2x2 matrix:


         1     2
P= 1  .95 .05
     2  .01. 99

If I were to convert this matrix to a 2-step transition probability
matrix I would get:

                1     2
P^2 = 1  .90 .10
          2  .02  .98

Is there a way to use [R] to calculate the nth step of a given  
matrix?

Thanks,

-Brad