The Perron-Frobenius Theorem revisited

An extension of the Perron-Frobenius Theorem is presented in the much more general setting of indecomposable semigroups of nonnegative matrices. Many features of the original theorem including the existence of a fixed positiv e vector, a block-monomial form, and spectral stability properties hold sim ultaneously for these semigroups. The paper is largely self-contained and t he proofs are elementary. The classical theorem and some related results fo llow as corollaries.