矩阵初等变换的几何意义  

Geometric meaning of elementary transformation of matrix

作　　者：雍龙泉[1] YONG Longquan(School of Mathematics and Computer Science,Shaanxi University of Technology,Hanzhong 723001,China)

机构地区：[1]陕西理工大学数学与计算机科学学院,陕西汉中723001

出　　处：《高师理科学刊》2024年第1期85-88,共4页Journal of Science of Teachers＇College and University

基　　金：陕西高等教育教学改革研究项目(21BZ013);陕西理工大学研究生教育教学改革研究项目(SLGYJG2306);陕西理工大学本科教育教学改革研究项目(XJG2304)。

摘　　要：矩阵的初等变换在线性代数中应用十分广泛,以初等行变换为例,分别给出了非退化的初等变换、退化的初等变换的实例与对应的几何图形,在此基础上给出了任意角度的旋转.在教学过程中,通过挖掘初等变换的几何意义,可以使学生建立代数与几何的统一观,促进学生抽象思维与形象思维协调发展.he elementary transformation of matrix is widely used in linear algebra.Taking the elementary row transformation as an example,the examples of the non-degenerate elementary transformation,the degenerate elementary transformation and the corresponding geometric figures are given,On this basis,rotation at any angle is provided.In the teaching process,by exploring the geometric significance of elementary transformations,it can help students to establish a unified view of algebra and geometry,and promote the coordinated development of abstract thinking and visual thinking.

关 键 词：矩阵 初等变换 几何意义 旋转 

分 类 号：O151[理学—数学] G642.0[理学—基础数学]