对偶空间、转置映射与一般线性群下的逆变向量和协变向量  

The dual space,the transposed mapping,and the contravariant and the covariant vectors of the general linear group

作　　者：涂泓[1,2] 冯承天[1] TU Hong;FENG Chengtian(Mathematics and Science College,Shanghai Normal University,Shanghai 200234,China;Key Lab for Astrophysics,Shanghai Normal University,Shanghai 200234,China)

机构地区：[1]上海师范大学数理学院,上海200234 [2]上海师范大学上海市星系和宇宙学半解析研究重点实验室,上海200234

出　　处：《上海师范大学学报（自然科学版）》2022年第4期397-400,共4页Journal of Shanghai Normal University(Natural Sciences)

摘　　要：从线性代数中的对偶空间出发,阐明了转置映射和转置矩阵等不为物理工作者所熟悉的概念.在此基础上,给出了一般线性群GL(n,K)下的逆变向量与协变向量,及其分量的变换法则.In this paper,the concepts of the dual space and the transposed mapping in linear algebra were enunciated,which were not well known by physicists.Based on the proposed concepts,two kinds of vectors named as contravariant vector and covariant vector for the general linear group and their transformation laws were fully explained and illustrated.

关 键 词：对偶空间 转置映射 逆变向量 协变向量 一般线性群 

分 类 号：O411.1[理学—理论物理]