The joint numerical range of commuting matrices
Volume 267 / 2022
Studia Mathematica 267 (2022), 241-259
MSC: Primary 15A60; Secondary 47A12, 47A20.
DOI: 10.4064/sm200622-31-5
Published online: 4 August 2022
Abstract
It is shown that for $n \le 3$ the joint numerical range of a family of commuting $n\times n$ complex matrices is always convex; for $n \ge 4$ there are two commuting matrices whose joint numerical range is not convex.
