Quaternionic numerical range of complex matrices
Functional Analysis
2020-08-10 v1
Abstract
The paper explores further the computation of the quaternionic numerical range of a complex matrix. We prove a modified version of a conjecture by So and Tompson. Specifically, we show that the shape of the quaternionic numerical range for a complex matrix depends on the complex numerical range and two real values. We establish under which conditions the bild of a complex matrix coincides with its complex numerical range and when the quaternionic numerical range is convex.
Cite
@article{arxiv.2008.02850,
title = {Quaternionic numerical range of complex matrices},
author = {Luís Carvalho and Cristina Diogo and Sérgio Mendes},
journal= {arXiv preprint arXiv:2008.02850},
year = {2020}
}