论文信息 - When is the numerical range of a nilpotent matrix circular?

When is the numerical range of a nilpotent matrix circular?

The problem formulated in the title is investigated. The case of nilpotent matrices of size at most 4 allows a unitary treatment. The numerical range of a nilpotent matrix M of size at most 4 is circular if and only if the traces trM^*M^2 and trM^*M^3 are null. The situation becomes more complicated as soon as the size is 5. The conditions under which a 5x5 nilpotent matrix has circular numerical range are thoroughly discussed.

Mihaela T. Matache | Valentin Matache

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