A note on convexity of sections of quaternionic numerical range

Authors

P. Santhosh Kumar, Indian Statistical Institute Bangalore

Article Type

Research Article

Publication Title

Linear Algebra and Its Applications

Abstract

The quaternionic numerical range of matrices over the ring of quaternions is not necessarily convex. We prove Toeplitz-Hausdorff like theorem: for any given quaternionic matrix, every section of its quaternionic numerical range is convex. We provide some additional equivalent conditions for the quaternionic numerical range of matrices over quaternions to be convex and prove some numerical radius inequalities.

First Page

92

Last Page

116

DOI

10.1016/j.laa.2019.03.005

Publication Date

7-1-2019

Comments

Open Access, Green

Recommended Citation

Santhosh Kumar, P., "A note on convexity of sections of quaternionic numerical range" (2019). Journal Articles. 793.
https://digitalcommons.isical.ac.in/journal-articles/793