浅谈几种求逆矩阵的方法  

Discussion on Several Methods of Finding Inverse Matrix

作　　者：徐晓静 

机构地区：[1]沈阳师范大学,辽宁 沈阳

出　　处：《应用数学进展》2021年第9期3217-3224,共8页Advances in Applied Mathematics

摘　　要：矩阵求逆作为线性代数的一个重要研究内容,在通信工程、计算机、物理学等领域有着广泛的应用。矩阵是大学数学中很重要的一个内容,在《高等代数》中我们学习了矩阵的一些基本知识及应用,而矩阵求逆的方法是矩阵中一个很重要的部分,那么如何判断一个矩阵是否可逆,怎样快速的去求解矩阵的逆,前人也总结了一些非常实用的方法。本文结合自身所掌握的知识,结合一些有代表性的例子进行说明,为了更便捷地解决求矩阵的逆,本文根据不同矩阵的不同特点简单介绍了几种求逆矩阵的方法:定义法、伴随矩阵法、初等变换法、分块矩阵法,同时也找出了一类特殊矩阵求逆的方法。As an important research content of linear algebra, matrix inverse is widely used in communication engineering, computer, physics and other fields. Matrix is an important content in university mathematics, in the “advanced algebra”, we learned some basic knowledge and application of matrix, the matrix inversion method is a very important part of the matrix, so how to determine whether a matrix is reversible, how to quickly to solve the inverse of the matrix, predecessors also summarize some very practical method. The text is explained in combination with its own knowledge and some representative examples. In order to solve the inverse matrix more conveniently, this paper simply introduces several methods of inverse matrix according to the different characteristics of different matrices: definition method, adjoint matrix method, elementary transformation method, partition matrix method. At the same time, the inverse method of a special kind of matrix is found.

关 键 词：矩阵的逆 初等变换 伴随矩阵 分块矩阵 初等循环矩阵 

分 类 号：O15[理学—数学]