初等矩阵的探析  

Analysis of Elementary Matrix

作　　者：何朝葵[1] 朱永忠[1] 柳庆新[1] HE Zhao-kui;ZHU Yong-zhong;LIU Qing-xin(College of Sciences, Hohai University, Nanjing 211100, China)

机构地区：[1]河海大学理学院,南京211100

出　　处：《大学数学》2020年第6期63-66,共4页College Mathematics

基　　金：国家自然基金(11571092);江苏省高等教育教学改革研究课题重点课题(2019JSJG086)。

摘　　要：从向量空间基的角度来探析三类初等矩阵,把一个初等矩阵理解成由自然基到一个特殊类型基的过渡矩阵,并通过一个正方体图形在三类初等线性变换下的变化来展示三类坐标变换的效果,然后通过对基的初等变换来求矩阵的逆.From the perspective of the basis of a vector space an elementary matrix is analyzed which is regarded as a transition matrix from a natural basis to a special type of basis.The effect of coordinate transformation is demonstrated by changing the figure of a cube.Then the calculation of inverse matrix is obtained through the elementary transformation of the base.

关 键 词：初等矩阵 基 线性变换 逆矩阵 

分 类 号：O172[理学—数学]