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arXiv · 1407.7564

Continuity of the Perron Root

Carl D. Meyer
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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.

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Carl D. Meyer. 2014-07-28. Continuity of the Perron Root. https://doi.org/10.1080/03081087.2014.934233

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