2017/05/02 by Stephan Weis, Weis, Stephan
Computer Science · Engineering · Mathematics · Physics and Astronomy · #14P05 #47A12 #81P16 #Advanced Numerical Analysis Techniques #Advanced Optimization Algorithms Research #Algebraic Geometry (math.AG) #FOS: Mathematics #FOS: Physical sciences #Operator Algebras (math.OA) #Polynomial and algebraic computation #Quantum Physics (quant-ph) #math.AG #math.OA #msc:14P05 #msc:47A12 #msc:81P16 #quant-ph
paper · pdf · doi:10.48550/arxiv.1705.00935
7 pages
arxiv created 2017/05/02 · openalex publication_date 2017/05/02 · arxiv updated 2017/05/03 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Kippenhahn discovered a real algebraic plane curve whose convex hull is the numerical range of a matrix. The correctness of this theorem was called into question when Chien and Nakazato found an example where the spatial analogue fails. They showed that the mentioned plane curve indeed lies inside the numerical range. We prove the easier converse direction of the theorem. Finding higher-dimensional generalizations of Kippenhahn's theorem is a challenge in real algebraic geometry.