Localization theorems for matrices and bounds for the zeros of polynomials over a quaternion division algebra

Abstract

In this paper, Ostrowski and Brauer type theorems are derived for the left and right eigenvalues of a quaternionic matrix. Generalizations of Gerschgorin type theorems are discussed for the left and the right eigenvalues of a quaternionic matrix. Thereafter a sufficient condition for the stability of a quaternionic matrix is given that generalizes the stability condition for a complex matrix. Finally, a characterization of bounds for the zeros of quaternionic polynomials is presented.