矩阵求逆方法探究
Method of Matrix Inversion
吕淑婷 1马泽玲1
作者信息
- 1. 北方民族大学 数学与信息科学学院,宁夏 银川 750021
- 折叠
摘要
矩阵在高等代数中占有很重要的地位,是主要研究对象与研究工具,许多问题最终可化归为矩阵及其运算问题,而矩阵求逆是矩阵运算的核心问题.本文总结了矩阵求逆的常规方法:定义法、伴随矩阵法、初等变换法、待定元素法、公式法、借助计算机求逆之外,给出了几种其它的方法:矩阵分块法、利用Hamilton-Cayley定理、多项式法、利用Sherman-Morrison公式,并辅助例题加以阐述.拓宽了矩阵求逆的方法,为学习、教学提供更多参考.
Abstract
Matrix plays an important role in advanced algebra and is the main research object and research tool.Many problems can be reduced to matrix and its operation,and matrix inversion is the core of matrix operation.The conventional methods of matrix inversion are summarized in this paper,including definition method,adjoint matrix method,elementary transformation method,undetermined element method,formula method and computer-aided inversion method.In addition,some other methods were given,such as matrix partition method,Hamilton-Cayley theorem,polynomial method and Sherman-Morrison formula,decomposition matrix inverse method,and auxiliary examples are elaborated.The study expandes the method of matrix inversion and provides more reference for learn-ing and teaching.
关键词
逆矩阵/Hamilton-Cayley定理/多项式法/Sherman-Morrison公式Key words
inverse matrix/Hamilton-Cayley theorem/Polynomial method/Sherman-Morrison formula引用本文复制引用
基金项目
宁夏回族自治区自然科学基金(2022AAC03265)
宁夏回族自治区哲学社会科学规划项目(20NXBYJ05)
宁夏宁夏回族自治区一流建设学科(数学)大学生思想政治教育研究课题(sxylxksz202110)
宁夏宁夏回族自治区一流课程建设项目()
出版年
2024
NETL
NSTL
万方数据