On the polynomial numerical hull of a normal matrix

Abstract

Let $A$ be any n-by-n normal matrix and let $k>0$ be an integer. By using the concept of the joint numerical range $W(A, A^2, \cdots, A^k),$ an analytic description of $V^k(A)$ for normal matrices will be presented. Additionally, new proof for Theorem 2.2 of Davis, Li and Salemi [Linear Algebra Appl., 428 (2008), pp. 137-153] is given.