  Let M be a b*b nonzero {0,1}-matrix. Let \rho(M) be its spectral radius and
let |M^n| be the norm of its n-th iteration. In the case \rho(M)>1, we see from
the spectral radius formula that {|M^n|}_{n=1}^\infty tends to \infty
exponentially as n to \infty. In the case \rho(M)=1, {|M^n|}_{n=1}^\infty can
be bounded or tend to \infty depending on M. The fine behavior of this sequence
is completely characterized in the present paper.
