Article
When is the numerical range of a nilpotent matrix circular?
Applied Mathematics and Computation
Document Type
Article
Publication Date
3-1-2010
Disciplines
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 5×5nilpotent matrix has circular numerical range are thoroughly discussed.
Citation Information
Valentin Matache and Mihaela Teodora Matache. "When is the numerical range of a nilpotent matrix circular?" Applied Mathematics and Computation Vol. 216 Iss. 1 (2010) p. 269 - 275 Available at: http://works.bepress.com/mihaela-velcsov/6/
This article was originally published here: http://www.sciencedirect.com/science/article/pii/S0096300310000652.
© 2010. This manuscript version is made available under the CC-BY-NC-ND 4.0 licensehttp://creativecommons.org/licenses/by-nc-nd/4.0/