Complex Roots of Quaternion Polynomials

2015/01/13 by Petroula Dospra, Dospra, Petroula, Dimitrios Poulakis +1
Mathematics · #11R52 #12E15 #16H05 #FOS: Mathematics #Rings and Algebras (math.RA) #math.RA #msc:11R52 #msc:12E15 #msc:16H05

paper · pdf · doi:10.48550/arxiv.1501.02942

arxiv created 2015/01/13 · arxiv updated 2015/01/14

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 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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