Quaternion polar representation with a complex modulus and complex argument inspired by the Cayley-Dickson form - Mathematics > Rings and AlgebrasReport as inadecuate




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Abstract: We present a new polar representation of quaternions inspired by theCayley-Dickson representation. In this new polar representation, a quaternionis represented by a pair of complex numbers as in the Cayley-Dickson form, buthere these two complex numbers are a complex -modulus- and a complex-argument-. As in the Cayley-Dickson form, the two complex numbers are in thesame complex plane using the same complex root of -1, but the complex phaseis multiplied by a different complex root of -1 in the exponential function. Weshow how to calculate the amplitude and phase from an arbitrary quaternion inCartesian form.



Author: Stephen J. Sangwine, Nicolas Le Bihan

Source: https://arxiv.org/







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