旋转矩阵群对应的李代数so(n)的型心与拟型心  

Centroids and Quasi-Centroids of Lie Algebra so(n) Corresponding to Rotation Matrix Group

作　　者：韩泽晟 王敏[1] 郑克礼[1] 

机构地区：[1]东北林业大学数学系,黑龙江 哈尔滨

出　　处：《理论数学》2023年第8期2325-2329,共5页Pure Mathematics

摘　　要：本文主要研究了刚体运动中旋转矩阵群对应的李代数so(n)的型心与拟型心。先应用解线性方程组的方法,计算出了3维李代数so(3)的型心与拟型心。接下来把so(3)的结论推广到so(n)中。最终,完全确定了so(n)型心与拟型心的矩阵表示。This paper mainly studies the centroids and quasi-centroids of the Lie algebra so(n) corre-sponding to the Rotation matrix group in rigid motion. Firstly, the centroids and quasi-centroids of the 3-dimensional Lie algebra so(3) are calculated by using the method of solving system of linear equations. Next, the conclusion of so(3) is extended to so(n). Finally, the matrix representation of so(n) centroids and quasi-centroids is completely determined.

关 键 词：李代数 型心 拟型心 矩阵表示 

分 类 号：R54[医药卫生—心血管疾病]