Bounds for the Zeros of Quaternionic Polynomials and Regular Functions Using Matrix Techniques

2024/12/18 by N. A. Rather, Rather, N. A., Wani Naseer +1
Physics and Astronomy · Mathematics · Computer Science · #Advanced Mathematical Theories and Applications #Algebraic and Geometric Analysis #Matrix Theory and Algorithms

paper · pdf · doi:10.48550/arxiv.2412.13827

Abstract

We investigate the problem of determining the zeros of quaternionic polynomials using matrix method. In a recent paper, Dar et al. \citeRD proved that the zeros of a quaternionic polynomial and the left eigenvalues of the corresponding companion matrix are identical. Building on this, we employ various newly developed matrix techniques to establish several results concerning the location of the zeros of regular polynomials of a quaternionic variable with quaternionic coefficients. These findings significantly enhance the understanding of quaternionic polynomials and their eigenvalues, offering a broader perspective on their mathematical properties.

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