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arXiv · 1501.02942

Complex Roots of Quaternion Polynomials

Petroula Dospra·Dimitrios Poulakis
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Abstract

The polynomials with quaternion coefficients have two kind of roots: isolated and spherical. A spherical root generates a class of roots which contains only one complex number $z$ and its conjugate $\bar{z}$, and this class can be determined by $z$. In this paper, we deal with the complex roots of quaternion polynomials. More precisely, using Bézout matrices, we give necessary and sufficient conditions, for a quaternion polynomial to have a complex root, a spherical root, and a complex isolated root. Moreover, we compute a bound for the size of the roots of a quaternion polynomial.

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Petroula Dospra, Dimitrios Poulakis. 2015-01-13. Complex Roots of Quaternion Polynomials. https://arxiv.org/abs/1501.02942

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