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 trMM2 and trMM3 are null. The situation becomes more complicated as soon as the size is 5. The conditions under which a 5

• Type: Journal
• Year: 2010
• Where: AMC
• Authors: Valentin Matache, Mihaela T. Matache
• Keywords: AMC 2010, Nilpotent Matrix, Numerical Range, Unitary Treatment