In this note, analytic description of V 3(A) is given for normal matrices of the form A = A1* iA2 or A = A1* ei23π A2* ei43π A3, where A1,A 2,A3 are Hermitian matrices. The new concept "k th roots of a convex set" is used to study the polynomial numerical hulls of order κ for normal matrices.
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Afshin, H. R., Mehrjoofard, M. A., & Salemi, A. (2009). Polynomial numerical hulls of order 3. Electronic Journal of Linear Algebra, 18, 253–263. https://doi.org/10.13001/1081-3810.1310