27 Sep
2006
27 Sep
'06
12:21 p.m.
In answer to my question << For each positive integer n > 0, what is the maximum value of N for which there exists an n-by-n posipotent stochastic matrix A such that the matrix A^N has all its entries positive but the matrices I , A , A^2 , ... , A^(N-1) do not?
Dan replied << The answer is n^2 - 2n + 2.
Can Dan (or someone else) provide a proof or a reference? Jim