  That the Perron root of a square nonnegative matrix A varies continuously
with the entries in A is a corollary of theorems regarding continuity of
eigenvalues or roots of polynomial equations, the proofs of which necessarily
involve complex numbers. But since continuity of the Perron root is a question
that is entirely in the field of real numbers, it seems reasonable that there
should exist a development involving only real analysis. This article presents
a simple and completely self-contained development that depends only on real
numbers and first principles.
