Kippenhahn's construction revisited
Functional Analysis
2023-09-01 v2 Algebraic Geometry
Abstract
Kippenhahn discovered that the numerical range of a complex square matrix is the convex hull of a plane real algebraic curve. Here, we present an example of a convex set, which has a similar algebraic description as the numerical range, whereas the analogue of Kippenhahn's construction fails regarding isolated, singular points of the curve. This example prompted us to carefully review Kippenhahn's assertion and to highlight aspects of a complete proof that was achieved with methods of convex geometry and real algebraic geometry.
Cite
@article{arxiv.2301.05802,
title = {Kippenhahn's construction revisited},
author = {Stephan Weis},
journal= {arXiv preprint arXiv:2301.05802},
year = {2023}
}
Comments
10 pages, accepted for publication in the proceedings of IWOTA 2022