When is the numerical range of a nilpotent matrix circular? |
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Authors: | Valentin Matache Mihaela T Matache |
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Institution: | Department of Mathematics, University of Nebraska, Omaha, NE 68182, USA |
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Abstract: | 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 tr M∗M2 and tr M∗M3 are null. The situation becomes more complicated as soon as the size is 5. The conditions under which a 5×5 nilpotent matrix has circular numerical range are thoroughly discussed. |
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Keywords: | Primary 15A60 Secondary 47A12 |
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