Dual Quaternions and Dual Quaternion Vectors

Liqun Qi; Chen Ling; Hong Yan

doi:10.1007/s42967-022-00189-y

Communications on Applied Mathematics and Computation ›› 2022, Vol. 4 ›› Issue (4) : 1494-1508. DOI: 10.1007/s42967-022-00189-y

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Dual Quaternions and Dual Quaternion Vectors

Liqun Qi¹^,² ,
Chen Ling¹^,b ,
Hong Yan³

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Abstract

We introduce a total order and an absolute value function for dual numbers. The absolute value function of dual numbers takes dual number values, and has properties similar to those of the absolute value function of real numbers. We define the magnitude of a dual quaternion, as a dual number. Based upon these, we extend 1-norm, $\infty$-norm, and 2-norm to dual quaternion vectors.

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Liqun Qi, Chen Ling, Hong Yan. Dual Quaternions and Dual Quaternion Vectors. Communications on Applied Mathematics and Computation, 2022, 4(4): 1494‒1508 https://doi.org/10.1007/s42967-022-00189-y