汇报标题 (Title)：Dual Quaternions and Augmented Quaternions （对偶四元数及增光四元数）
汇报人 (Speaker)：祁力群 教授（香港理工大学、荆门电子科技大学）
汇报功夫 (Time)：2023年10月16日(周一) 9:00-11:00
汇报地址 (Place)：校本部F309会议室
约请人(Inviter)：王卿文 教授
主办部门：理学院数学系
汇报提要：In this talk, I will first report our work on eigenvalues of Hermitian dual quaternion matrices. This work extends the classical theory of eigenvalues of Hermitian complex matrices and Zhang's 1997 result on eigenvalues of Hermitian quaternion matrices. Then we apply this result to the formation control study, while formation control is very important in the UAV research. Then I will report our work on augmented quaternions, and formulate hand-eye calibration, which is a basic problem in robotic research, and SLAM (Simultaneous Location and Mapping), which is a very hot topic in robotic research, as equality constrained augmented dual quaternion optimization problems. This approach reduces the size of the
problem and keep the smoothness of the model. We explore these two directions from two different points of view to quaternions and dual quaternions. In this talk, I will explain these two different points of view.
