MATH307 April 2012
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Question 08 (b)
Consider the stochastic matrix
(b) By considering P2, what can you say about the other eigenvalues of P? Give a reason.
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We will begin by calculating what is:
We know that one of the properties of a stochastic matrix is, if or some power has all positive entries (that is, no zero entries) then the other eigenvalues of besides will have (referenced from page 187 of the current 2014 Summer Math 307 Textbook). Since we just found that all the entries in are positive, we can see that the other eigenvalues of must follow: .