Suppose that the transition matrix P of a Markov chain is given by

Use the definitions (B. 45) and (B .46) to find the (two) eigenvalues and the (two pairs of) corresponding left and right eigenvectors of P.

Solution

By using quadratic equation;

Now for the eigenvectors

For the two state chain of symmetric formulism the multiplicative identity for “i” number of iteration is given, by using the induction the equation becomes