When is the numerical range of a nilpotent matrix circular?

Authors

Valentin Matache, University of Nebraska at OmahaFollow
Mihaela Teodora Matache, University of Nebraska at OmahaFollow

Document Type

Article

Publication Date

3-2010

Publication Title

Applied Mathematics and Computation

Volume

216

Issue

1

First Page

269

Last Page

275

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.

Comments

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/

Recommended Citation

Matache, Valentin and Matache, Mihaela Teodora, "When is the numerical range of a nilpotent matrix circular?" (2010). Mathematics Faculty Publications. 24.
https://digitalcommons.unomaha.edu/mathfacpub/24