关于线性变换及其矩阵的一点注记

A Few Notes on Linear Transformations and Their Matrices

摘要: 线性变换及其矩阵是高等代数的精华内容，也是该课程教与学的一个难点。在线性变换与其矩阵的对应关系基础上，建立欧氏空间上正交变换与正交矩阵、镜面反射变换与镜面反射矩阵、对称变换与实对称矩阵等的1-1对应关系，帮助学生开拓思路、化抽象为具体，提升用矩阵方法和技巧处理线性变换问题的能力。

Abstract: Linear transformations and their matrices are the essential content of advanced algebra, and also a difficult point in the teaching and learning of this course. Based on the bijective correspondence between linear transformations and their matrices, one-to-one corresponding relationships are established, such as those between orthogonal transformations and orthogonal matrices in Euclidean spaces, between mirror reflection transformations and mirror reflection matrices, and between symmetric transformations and real symmetric matrices. This helps students broaden their thinking, transform the abstract into the concrete, and enhance their ability to handle problems related to linear transformations using matrix methods and techniques.