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edited May 11, 2023 at 19:53

2.7k
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...or prove that none exists.

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

Stochastic matrices are, by definition, nonnegative.

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edit approved Jun 9, 2017 at 18:14

Pietro Paparella

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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

linear-algebra matrices stochastic-processes eigenvalues matrix-theory nonnegative-matrices

Post Undeleted by Gerry Myerson, Todd Trimble

occurred Apr 14, 2016 at 0:45

Post Deleted by tarski

occurred Apr 12, 2016 at 4:28

added 189 characters in body

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edited Apr 12, 2016 at 4:14

tarski

121
3

...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.