The quaternionic Gauss-Lucas Theorem
Complex Variables
2022-04-26 v2
Abstract
The classic Gauss-Lucas Theorem for complex polynomials of degree has a natural reformulation over quaternions, obtained via rotation around the real axis. We prove that such a reformulation is true only for . We present a new quaternionic version of the Gauss-Lucas Theorem valid for all , together with some consequences.
Cite
@article{arxiv.1712.00744,
title = {The quaternionic Gauss-Lucas Theorem},
author = {Riccardo Ghiloni and Alessandro Perotti},
journal= {arXiv preprint arXiv:1712.00744},
year = {2022}
}
Comments
7 pages, 1 figure. Remarks added in section 3. Proposition 14 added with complete proof