Think of it this way, you have a col. vector

with the probabilities of the

current nucloetide being A,C,G,T down the columns.

Then the stochastic

matrix will give you the probabilities for the nucloetide

at the next position as

.

So if the current nucloetide is A, the first column of

gives the probability

that next nucloetide is A, C, G or T, similarly if the current nucloetide is C

the second column gives the probability that next nucloetide is A, C, G or T,

and so on.

Now the numbers given for the transition probabilities in the question do

not run down the columns as described above but accross the rows, so:

You say that you can work out the eigen values and vectors yourself so

I will leave that to you.

A steady state is a vector

such that:

that is it is an eigen vector corresponding to an eigen value of

RonL