On the convexity and circularity of the numerical range of nilpotent quaternionic matrices
Functional Analysis
2019-08-01 v1
Abstract
We provide a sufficient condition for the numerical range of a nilpotent matrix N to be circular in terms of the existence of cycles in an undirected graph associated with N. We prove that if we add to this matrix N a diagonal real matrix D, the matrix D + N has convex numerical range. For 3 x 3 nilpotent matrices, we strength further our results and obtain necessary and sufficient conditions for circularity and convexity of the numerical range.
Keywords
Cite
@article{arxiv.1907.13438,
title = {On the convexity and circularity of the numerical range of nilpotent quaternionic matrices},
author = {Luís Carvalho and Cristina Diogo and Sérgio Mendes},
journal= {arXiv preprint arXiv:1907.13438},
year = {2019}
}