# [R] nth step transition matrices

Rolf Turner r.turner at auckland.ac.nz
Wed Apr 23 02:14:57 CEST 2008

```(a) Is this a homework question?

(b) Your value of P^2 is very rough --- only 2 decimal places.

(c) The answer to the question ``Is there a way ...?'' is ``Of course!''
There is always a way in R.

(d) In this case I would write a function, say ``matpow(M,n)'' to
calculate
the n-th power of M.

(e) I would use a for loop to do this.

(f) From here on, you're on your own.

cheers,

Rolf Turner

On 23/04/2008, at 11:49 AM, Brad Lukoskie wrote:

> 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,
>
>
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