| 一种基于矩阵初等变换的Schmidt正交化方法 |
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| 引用本文： | 何朝葵,朱永忠,柳庆新.一种基于矩阵初等变换的Schmidt正交化方法[J].大学数学,2021,37(2):42-47. |
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| 作者姓名： | 何朝葵 朱永忠 柳庆新 |
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| 作者单位： | 河海大学 理学院,南京 211100 |
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| 基金项目： | 江苏省高等教育教学改革研究课题重点课题 |
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| 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.
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| 关 键 词： | 合同变换 Schmidt正交化 初等变换 |
A Schmidt Orthogonalization Method Based on Elementary Transformations |
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| HE Zhao-kui,ZHU Yong-zhong,LIU Qing-xin.A Schmidt Orthogonalization Method Based on Elementary Transformations[J].College Mathematics,2021,37(2):42-47. |
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| Authors: | HE Zhao-kui ZHU Yong-zhong LIU Qing-xin |
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| Institution: | (College of Sciences,Hohai University,Nanjing 211100,China) |
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| Abstract: | 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. |
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| Keywords: | congruent transformation Schmidt orthogonalization elementary transformation |
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