矩阵初等变换在高等代数中的应用及教学研究  

The Application of the Elementary Transformation of Matrix in Advanced Algebra

作　　者：张芳英 朱睦正 Zhang Fang-ying;Zhu Mu-zheng(School of Mathematics and Statistics,Hexi University,Zhangye Gansu 734000)

机构地区：[1]河西学院数学与统计学院,甘肃张掖734000

出　　处：《河西学院学报》2020年第2期117-122,共6页Journal of Hexi University

基　　金：甘肃省精品资源共享课程建设项目;河西学院博士科研基金项目.

摘　　要：矩阵的初等变换是高等代数课程的重要组成部分,其思想贯穿于高等代数的始终,在矩阵的理论研究中占有非常重要的地位.本文主要讨论了矩阵初等变换在高等代数中矩阵的秩、矩阵的逆、线性方程组的解、二次型标准化和标准正交基等方面的应用,并就矩阵初等变换的教学进行了一些探讨,有利于进一步理解矩阵初等变换的思想,提升灵活应用矩阵初等变换法简化或解决实际问题的能力,夯实专业理论基础.The elementary transformation of the matrix is a very important component of Advanced Algebra. Its idea runs through the whole Advanced Algebra and plays an important role in the study of the matrix. This paper summarizes the applications of the elementary transformation in the matrix rank,the matrix inversion,the solution of the linear equations,the standard form of the quadratic form and the standard orthogonal basis,and the teaching method of the elementary transformation is discussed,which are helpful to understand the thought of the elementary transformation,improve the ability to simplify and solve an algebraic problem with the elementary transformation of the matrix,and consolidate the professional theoretical basis.

关 键 词：矩阵初等变换 矩阵的逆 线性方程组的解 二次型标准化 标准正交基 

分 类 号：O151.21[理学—数学]