The proof of Perron-Frobenius Theorem Can someone recommend me a book where I can find a detailed proof of the Perron-Frobenius Theorem for nonnegative matrices?

There must be many, but just to mention a couple of standard references on matrices:

* _Matrices: Theory and Applications_ by Denis Serre. (Sect. 8.2–3 in the second edition.)
* _Matrix Analysis_ by Horn & Johnson. (Sect. 8.4 in the second edition.)