spectral radius of matrix with elements less than one Assume we have a square matrix A whose elemnts are less than 1, Can we say that its spectral radius is also less than 1. Can we say that the absolute value of its eigenvalues are also less than 1?

Let $A= {9 \over 10} e e^T$, where $e$ is a vector of  ones. Then we have all elements have elements less than one, but $A e = {9 \over 10} n e$. Hence  for $n>1$, we have some eigenvalue $\lambda = {9 \over 10} n  > 1$.
