Continuity of the Perron Root
arXiv:1407.7564 · doi:10.1080/03081087.2014.934233
Abstract
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.
Received: 21 Feb 2014, Accepted: 9 Jun 2014, Published online: 03 Jul 2014, Linear and Multilinear Algebra, 2014