On Semi-tensor Product of Matrices and Its Applications

作     者：Dai-zhan Cheng, Li-jun ZhangInstitute of Systems Science, Academy of Mathematics and System Sciences, Chinese Academy of Sciences, Beijing 100080, P.R. China 

作者机构：Institute of Systems Science Academy of Mathematics and System Sciences Chinese Academy of Sciences Beijing P. R. China 

出 版 物：《Acta Mathematicae Applicatae Sinica》 (应用数学学报（英文版）)

年 卷 期：2003年第19卷第2期

页      面：219-228页

核心收录：

学科分类：07[理学] 070104[理学-应用数学] 0701[理学-数学] 

基　　金：Partially supported by the National Science Foundation (G.59837270) the National Key Project (G.1998020308) of China 

主　　题：Keywords Matrix semi-tensor product connection Christoffel symbol algebra 

摘      要：Abstract The left semi-tensor product of matrices was proposed in [2]. In this paper the right semi-tensor product is introduced first. Some basic properties are presented and compared with those of the left semi-tensor *** two new applications are investigated. Firstly, its applications to connection, an important concept in differential geometry, is considered. The structure matrix and the Christoffel matrix are introduced. The transfer formulas under coordinate transformation are expressed in matrix form. Certain new results are obtained. Secondly, the structure of finite dimensional Lie algebra, etc. are investigated under the matrix *** applications demonstrate the usefulness of the new matrix products.