...or prove that none exists.
The matrix
0 1
1 0
is the obvious example when M can have size 2.
Note that M can't be primitive so there is at least one entry equal to zero in every power M^k (Perron-Frobenius).
Thank you.
Ex. of square, stochastic matrix (w/ non-neg entries) of odd size, not a permutation matrix, with an eigenvalue other than 1 on the unit circle.
tarski
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