Computation of the zeros of a quaternionic polynomial using matrix methods

Abstract

In 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

Mathematics Subject Classification (2020):

• 30A10
• 30C10
• 30C15

Acknowledgement

The author’s are highly grateful to the referees for their valuable suggestions and comments which has improved the quality of this work.

Author’s contributions

All authors contributed equally to the writing of this paper. All authors read and approved the final manuscript.

Disclosure statement

The authors declare that they have no competing interests.