从一道课本例题谈矩阵求逆  

On Matrix Inverse Inspired by an Example

作　　者：尹小艳 YIN Xiaoyan(School of Mathematics and Statistics,Xidian University,Xi'an 710071)

机构地区：[1]西安电子科技大学数学与统计学院,陕西西安710071

出　　处：《高等数学研究》2023年第5期17-20,共4页Studies in College Mathematics

基　　金：西安电子科技大学高等代数省级一流课程建设项目;西安电子科技大学研究生矩阵分析与计算核心课程建设项目.

摘　　要：对一道分块矩阵求逆的课本习题,给出一种简便的新解法,进一步拓展,得到几个重要的矩阵和式求逆公式.总结矩阵求逆的常用理论方法,帮助学生全方位掌握矩阵求逆技巧.A simple method is offered to calculate the inverse of a general 2×2 partitioned matrix.Moreover,some new expressions for the inverse of a sum-matrix are obtained.A summary of commonly used methods of matrix inverse computing are provided and several special examples are illustrated.This work may lead to more comprehensive and efficient calculating of matrix inverse.

关 键 词：逆矩阵 分块矩阵 初等变换 

分 类 号：O151.2[理学—数学]