The joint numerical range of commuting matrices
Pan-Shun Lau, Chi-Kwong Li, Yiu‐Tung Poon · Studia Mathematica · 2022
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.