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Split Quaternion Matrix Representation of Dual Split Quaternions and Their Matrices [PDF]

Advances in Applied Clifford Algebras, 2015
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Melek Erdogdu, Mustafa Özdemir, Özdemir Mustafa   +2 more
exaly   +3 more sources

Dual Quaternions and Dual Quaternion Vectors

Communications on Applied Mathematics and Computation, 2022
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.
Liqun Qi, Chen Ling, Hong Yan
exaly   +3 more sources

The geometric structure of unit dual quaternion with application in kinematic control

Journal of Mathematical Analysis and Applications, 2012
In this paper, the geometric structure, especially the Lie-group related properties, of unit dual quaternion is investigated. The exponential form of unit dual quaternion and its approximate logarithmic mapping are derived. Correspondingly, Lie-group and
Xiangke Wang, Changbin Yu
exaly   +3 more sources

Solving the QLY Least Squares Problem of Dual Quaternion Matrix Equation Based on STP of Dual Quaternion Matrices

Symmetry
Dual algebra plays an important role in kinematic synthesis and dynamic analysis, but there are still few studies on dual quaternion matrix theory. This paper provides an efficient method for solving the QLY least squares problem of the dual quaternion ...
Ruyu Tao, Mingcui Zhang, Musheng Wei
exaly   +2 more sources

Moore determinant of dual quaternion Hermitian matrices

Computational and Applied Mathematics
In this paper, we extend the Chen and Moore determinants of quaternion Hermitian} matrices to dual quaternion Hermitian matrices. We show the Chen determinant of dual quaternion Hermitian {matrices is invariant under addition, switching, multiplication ...
Chunfeng Cui, Liqun Qi, Guangjing Song   +2 more
exaly   +2 more sources

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Involutions in Dual Split-Quaternions

Advances in Applied Clifford Algebras, 2015
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Bekar, MURAT, Yayli, Yusuf
openaire   +2 more sources

Dual Quaternion Matrix Equation AXB = C with Applications

Symmetry
Dual quaternions have wide applications in automatic differentiation, computer graphics, mechanics, and others. Due to its application in control theory, matrix equation AXB=C has been extensively studied.
Qing-Wen Wang, Lv-Ming Xie, Wang Qing-Wen   +2 more
exaly   +2 more sources

Comparison of strapdown inertial navigation algorithm based on rotation vector and dual quaternion

Chinese Journal of Aeronautics, 2013
For the navigation algorithm of the strapdown inertial navigation system, by comparing to the equations of the dual quaternion and quaternion, the superiority of the attitude algorithm based on dual quaternion over the ones based on rotation vector in ...
Zhenhuan, Wang, Xijun, Chen, Qingshuang, Zeng   +2 more
exaly   +2 more sources