When is the numerical range of a nilpotent matrix circular?

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• 作者：Valentin Matache ; Mihaela T. Matache
• 关键词：Nilpotent matrix ; Numerical range
• 刊名：Applied Mathematics and Computation
• 出版年：2010
• 出版时间：1 March 2010
• 年：2010
• 卷：216
• 期：1
• 页码：269-275
• 全文大小：231 K

文摘

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.