BOUNDS ON THE ZEROS OF A QUATERNIONIC POLYNOMIAL USING MATRIX METHODS

Abstract

In this paper, the problem of locating the left eigenvalues of the quaternion matrices and their connection with the zeros of the quaternion polynomials with quaternion coecients is considered by using various matrix tools. As an application of which, various famous results for locating the zeros of regular polynomials of a quaternionic variable with quaternionic coecients are obtained, which include the extension of Cauchy's theorem, Parodi's theorem as well.