Skip to main content
9 of 11
added 189 characters in body

Find a square, stochastic matrix (w/ non-neg entries) of odd size, not a permutation matrix, with an eigenvalue other than 1 on the unit circle

...or prove that none exists.

Note that such a matrix M couldn't be primitive, so there would be at least one entry equal to zero in every power M^k (Perron-Frobenius theory).

Preferably the matrix would have a diagonal that is not all zero, and at the risk of making the problem imprecise, I'd like to find such a matrix with as few zeros and ones as possible.

Thank you.