The convex algebraic geometry of higher-rank numerical ranges
Functional Analysis
2024-10-30 v1 Algebraic Geometry
Abstract
The higher-rank numerical range is a convex compact set generalizing the classical numerical range of a square complex matrix, first appearing in the study of quantum error correction. We will discuss some of the real algebraic and convex geometry of these sets, including a generalization of Kippenhahn's theorem, and describe an algorithm to explicitly calculate the higher-rank numerical range of a given matrix.
Keywords
Cite
@article{arxiv.2410.21625,
title = {The convex algebraic geometry of higher-rank numerical ranges},
author = {Jonathan Nino-Cortes and Cynthia Vinzant},
journal= {arXiv preprint arXiv:2410.21625},
year = {2024}
}
Comments
26 pages, 8 figures