有关初等矩阵的定理教学设计——基于“知识可视化”理念

Teaching Design of the Theorems Related to Elementary Matrices:Based on the Method of “Knowledge Visualization ”

有关初等矩阵的系列定理是连接矩阵乘积与矩阵初等变换的桥梁,是求逆矩阵、解矩阵方程等知识点的理论基础,亦是矩阵理论体系的核心定理之一。基于"知识可视化"的理念,借助动态图形变换、类比实际案例等教学手段,探究有关初等矩阵的定理的教学设计,建立初等矩阵与初等矩阵乘积运算之间的关系体系,实现知识的可视化,教学的体系化。

The theorems related to elementary matrices are the ligament connecting the product of matrices with the elementary transformation,also the theory foundation of finding inverse matrices and solving matrix equations,and one of the core theorems of theory system of matrices. Based on the method of ＂Knowledge Visualization ＂,the dynamic graphic changes and the analogy to practical examples,this paper study the teaching design on the theorems related to elementary matrices,construct the system of relationship between the product of matrices with the elementary transformation,and realize the visualization of knowledge and the systematization of teaching.