I found this proof of Perron Frobenius Theorem using Banach Fixed Point Theorem very elegant.
However, I can't quite get the claim (in the 6th line from the top on page 2) saying that
$(A|w|)$ is a vector with length smaller than $\lambda L$, where $L$ is the length of $w$
This claim makes sense to me if $\lambda$ is the maximum singular value but I think $\lambda$ is the maximum eigenvalue. And I think the matrix $A$ can be asymmetric and so the eigenvalues and singular values do not need to be the same. Am I missing something?
