矩阵秩的定义教学设计新探

A New Exploration of the Teaching Design of the Definition of the Rank of Matrix

矩阵的秩是线性代数中的一个重要的概念。区别于传统的矩阵秩的定义的教学设计,该文从矩阵的标准形是否唯一这一问题入手,将问题转化为初等变换是否改变矩阵非零子式的最高阶数这一问题,通过分析得到非零子式的最高阶数是初等变换过程中的不变量,从而引出了矩阵秩的概念。这样一种新的处理方式,不仅在引入上非常自然,而且能使学生认识到矩阵的秩的意义。从而使学生更容易理解这一抽象的概念,提高教学效果。

The rank of matrix is an important concept in linear algebra.In this paper,different from the traditional teaching design of the definition of matrix rank,we start with the problem of whether the standard form of matrix is unique or not,and then transform the problem into the problem of whether the primary transformation changes the highest order of the non-zero sub formula of matrix.Through analysis,we get that the highest order of the non-zero sub formula is the invariant in the process of the primary transformation,thus leading to the concept of matrix rank.Such new approach is not only very natural in introducing,but also enables students to recognize the meaning of the definition of the rank of matrix.Therefore,students can understand this abstract concept more easily and improve the teaching effect.