165 citations · 1.2k across the 132 of their papers we have counts for
133 papers
A Power Method for Computing the Dominant Eigenvalue of a Dual Quaternion Hermitian Matrix
Chunfeng Cui, Liqun Qi
In this paper, we first study the projections onto the set of unit dual quaternions, and the set of dual quaternion vectors with unit norms. Then we propose a power method for comp…
Motion, Unit Dual Quaternion and Motion Optimization
Liqun Qi
We introduce motions as real six-dimensional vectors. A motion means a rotation and a translation. We define a motion operator which maps unit dual quaternions to motions, and a UD…
Standard Dual Quaternion Optimization and Its Applications in Hand-Eye Calibration and SLAM
Liqun Qi
Several common dual quaternion functions, such as the power function, the magnitude function, the -norm function and the th largest eigenvalue of a dual quaternion Hermitian…
Dual Quaternion Matrices in Multi-Agent Formation Control
Liqun Qi, Xiangke Wang, Ziyan Luo
Three kinds of dual quaternion matrices associated with the mutual visibility graph, namely the relative configuration adjacency matrix, the logarithm adjacency matrix and the rela…
Low Rank Approximation of Dual Complex Matrices
Liqun Qi, David M. Alexander, Zhongming Chen +2
Dual complex numbers can represent rigid body motion in 2D spaces. Dual complex matrices are linked with screw theory, and have potential applications in various areas. In this pap…
Eigenvalues and Singular Values of Dual Quaternion Matrices
Liqun Qi, Ziyan Luo
The poses of robotics in time points may be represented by an dual quaternion matrix. In this paper, we study the spectral theory of dual quaternion matrices.…