Continuity of the Perron Root
Classical Analysis and ODEs
2014-07-30 v1
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.
Keywords
Cite
@article{arxiv.1407.7564,
title = {Continuity of the Perron Root},
author = {Carl D. Meyer},
journal= {arXiv preprint arXiv:1407.7564},
year = {2014}
}
Comments
Received: 21 Feb 2014, Accepted: 9 Jun 2014, Published online: 03 Jul 2014, Linear and Multilinear Algebra, 2014