[R] nth step transition matrices

[Brad Lukoskie]

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