## Matrices with almost constant coefficient have a simple eigenvalue

As a by-product of a general result for bounded operators of a Banach space, I have the following: A matrix $L=(\ell_{ij})_{ij}$ that has almost constant coefficients in the sense that for some $c$, on all row $i$ it holds \begin{equation} \frac{1}{n}\sum_k \lvert \ell_{ik}-c\rvert\le \frac{|c|}{6}, \label{eq:Perron} \end{equation} must have a simple eigenvalue. Under a slightly stronger … Read more