报告题目 (Title)：Dual Quaternions and Augmented Quaternions （对偶四元数及增光四元数）

报告人 (Speaker)：祁力群 教授（香港理工大学、杭州电子科技大学）

报告时间 (Time)：2023年10月16日(周一) 9:00-11:00

报告地点 (Place)：校本部F309会议室

邀请人(Inviter)：王卿文 教授

主办部门：理学院数学系

报告摘要：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.