Continuity of the Perron Root
| Autor: | Meyer, Carl D. |
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| Rok vydání: | 2014 |
| Předmět: |
Mathematics - Classical Analysis and ODEs
14J26 (Secondary) "Perron-Frobenius Theory" "Nonnegative Matrices" |
| Druh dokumentu: | Working Paper |
| DOI: | 10.1080/03081087.2014.934233 |
| Popis: | 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. Comment: Received: 21 Feb 2014, Accepted: 9 Jun 2014, Published online: 03 Jul 2014, Linear and Multilinear Algebra, 2014 |
| Databáze: | arXiv |
| Externí odkaz: |
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