Originally Posted by

**CaptainBlack** Think of it this way, you have a col. vector $\displaystyle X$ with the probabilities of the

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

Then the stochastic $\displaystyle S$ matrix will give you the probabilities for the nucloetide

at the next position as $\displaystyle SX$.

So if the current nucloetide is A, the first column of $\displaystyle S$ 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:

$\displaystyle

S=\left[ \begin{array}{cccc}

0.18&0.274&0.426&0.12\\

0.17&0.368&0.274&0.188\\

0.161&0.339&0.385&0.115\\

0.079&0.355&0.384&0.182

\end{array} \right]

$

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 $\displaystyle X$ such that:

$\displaystyle

SX=X

$

that is it is an eigen vector corresponding to an eigen value of $\displaystyle 1$

RonL