Dual Quaternions and Dual Quaternion Vectors

2021/11/08 by Liqun Qi, Qi, Liqun, Hong Yan +2 · 6 citations
Mathematics · #Algebraic and Geometric Analysis #FOS: Mathematics #Rings and Algebras (math.RA)

paper · pdf · doi:10.48550/arxiv.2111.04491

openalex publication_date 2021/11/08 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We introduce a total order and the absolute value function for dual numbers. The absolute value function of dual numbers are with dual number values, and have properties similar to the properties of the absolute value function of real numbers. We define the magnitude of a dual quaternion, as a dual number. Based upon these, we extended 1-norm, ∞-norm and 2-norm to dual quaternion vectors.

Cited by

• The Power Method for Non-Hermitian Dual Quaternion Matrices
• Generalized singular value decompositions of dual quaternion matrices and beyond
• A fragile zero-watermarking method based on dual quaternion matrix decomposition
• Orthogonal tripotent matrices
• Projecting onto the Unit Dual Quaternion Set
• A Dual Quaternion Control Law for Formation Control of Multiple 3-D Rigid Bodies

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• Projecting onto the Unit Dual Quaternion Set
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