Bounds for the Right Spectral Radius of Quaternionic Matrices

Abstract

In the present paper, we establish bounds for the sum of the moduli of right eigenvalues of a quaternionic matrix. As a consequence, we establish bounds for the right spectral radius of a quaternionic matrix. We also present a minimal ball in 4D spaces that contains all Geršgorin balls of a quaternionic matrix. As an application, we introduce the estimation for the right eigenvalues of quaternionic matrices in the minimal ball. Finally, we suggest some numerical examples to illustrate our results. © 2020, Springer Science+Business Media, LLC, part of Springer Nature.