Localization Theorems for Matrices and Bounds for the Zeros of Polynomials over 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.