Yet another proof that the roots of a polynomial depend continuously on the coefficients
Classical Analysis and ODEs
2022-07-08 v2 Rings and Algebras
Abstract
The roots of a complex polynomial depend continuously on the coefficients; that is, an infinitesimal perturbation of the coefficients results in an infinitesimal perturbation of the roots. A short, straightforward proof of this is possible using infinitesimals.
Keywords
Cite
@article{arxiv.2207.00123,
title = {Yet another proof that the roots of a polynomial depend continuously on the coefficients},
author = {David A. Ross},
journal= {arXiv preprint arXiv:2207.00123},
year = {2022}
}
Comments
6 pages. Clarifies some statements in an earlier version