Polynomial numerical hulls of order 3

Abstract

In this note, analytic description of V ³(A) is given for normal matrices of the form A = A₁⊕ iA₂ or A = A₁ ⊕ e^{i 2π/3} A2 ⊕ e^{i 4π/3} A₃, where A₁,A₂,A₃ are Hermitian matrices. The new concept “k^th roots of a convex set” is used to study the polynomial numerical hulls of order k for normal matrices.