Dual Quaternions and Dual Quaternion Vectors

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 Qi^1,2, Chen Ling¹, Hong Yan³

1. Department of Mathematics, School of Science, Hangzhou Dianzi University, Hangzhou, 310018, Zhejiang, China;
2. Department of Applied Mathematics, The Hong Kong Polytechnic University, Hung Hom, Kowloon, Hong Kong, China;
3. Department of Electrical Engineering and Centre for Intelligent Multidimensional Data Analysis, City University of Hong Kong, Kowloon, Hong Kong, China

Received:2021-11-16 Revised:2022-02-21 Online:2022-12-20 Published:2022-09-26
Supported by:
Liqun Qi:This author's work was supported by Hong Kong Innovation and Technology Commission (InnoHK Project CIMDA). Chen Ling:This author's work was supported by the National Natural Science Foundation of China (No. 11971138) and the Natural Science Foundation of Zhejiang Province of China (Nos. LY19A010019, LD19A010002). Hong Yan:This author's work was supported by Hong Kong Research Grants Council (Project 11204821), Hong Kong Innovation and Technology Commission (InnoHK Project CIMDA) and City University of Hong Kong (Project 9610034).

Abstract

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, ∞-norm, and 2-norm to dual quaternion vectors.

Key words: Dual number, Absolute value function, Dual quaternion, Magnitude, Norm

CLC Number:

Liqun Qi, Chen Ling, Hong Yan. Dual Quaternions and Dual Quaternion Vectors[J]. Communications on Applied Mathematics and Computation, 2022, 4(4): 1494-1508.

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Dual Quaternions and Dual Quaternion Vectors

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