Computation of the zeros of a quaternionic polynomial using matrix methods

Abstract

AbstractIn a recent paper, Ishfaq Dar (2024), worked on the problem of locating the zeros of quaternion polynomials by introducing various matrix techniques. In this paper, we use those newly developed matrix methods to locate the left eigenvalues of the quaternion companion matrix of the polynomial, which in turn yield various results concerning the location of the zeros of quaternionic polynomials including extensions of the results of Rubinstein and A. Aziz to the quaternionic setting as well.

Keywords

• Companion matrix
• quaternionic polynomials
• right (and left) quaternionic eigenvalues
• 30A10
• 30C10
• 30C15