Polynomial numerical hulls of order 3

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Hamid Reza Afshin
Mohammad Ali Mehrjoofard
Abbas Salemi


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

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