I am trying to prove that eigen values of row stochastic matrix/ column stochastic matrix/ doubly stochastic matrix need not be necessarily simple. Is there any mathematical proof?
Stochastic matrices
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linear-algebra
matrices
graph-theory
eigenvalues-eigenvectors
markov-chains
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0To show that a stochastic matrix need not have distinct eigenvalues, you just need to give an example of a stochastic matrix where at least one eigenvalue is repeated. – 2017-02-01
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0Try to work out what happens in the case when the underlying graph has two connected components. I think this might give you what you want. – 2017-02-01
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1You can consider as a (counter) example the identity matrix. The eigenvalue $\lambda = 1$ is semi - simple. – 2017-02-02
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1Also, you may find [this link](http://math.stackexchange.com/questions/1044491/stochastic-matrix-semisimple-eigenvalue) quite useful. – 2017-02-02