一种基于矩阵初等变换的Schmidt正交化方法  

A Schmidt Orthogonalization Method Based on Elementary Transformations

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》2021年第2期42-47,共6页College Mathematics

基　　金：江苏省高等教育教学改革研究课题重点课题(2019JSJG086)。

摘　　要：对向量组的Schmidt正交化法和合同变换法的关系进行了分析,指出Schmidt正交化法就是合同变换法中利用规范化初等变换后的一种特殊情况,由此给出一种基于矩阵初等变换的Schmidt正交化方法——Schmidt初等变换正交化法,以及这一方法在软件Matlab上实现的程序.The relationship between the Schmidt orthogonalization method and the congruent transformation method for orthogonalizing the vector group is analyzed.It is pointed out that the Schmidt orthogonalization method is a special case of the congruent transformation method by using normalized elementary transformation.Thus a novel orthogonalization method based on elementary transformation--Schmidt elementary transformation orthogonalization method is proposed and the procedure of this method on MATLAB are given.

关 键 词：合同变换 Schmidt正交化 初等变换 

分 类 号：O151[理学—数学]