

Comments
When we study eigenvalues and eigenvectors, we will learn some of the mathematical reasons for the results that you saw in this lab. In the process we will see how to do these computations theoretically (that is, without approximating limits by calculator or computer). We will also be able to see some of the mathematical justification for the following theorem, which tells why the Markov chains in Parts 1 and 2 approached a steady state and the one in this part did not.
Theorem
If A is a positive transition matrix (no zero entries), and p_{0} is any initial probability vector, then A^{k}p_{0} approaches the steadystate vector as k goes to infinity.

