引入交换图研究线性映射的像与核

Image and Core of Linear Mapping Through the Introduction of Interchange Graph

线性映射像与核的概念比较抽象,学生难以深刻洞悉其结构,现行教材中对Kerφ与Imφ的讨论非常少,故将交换图引入其中,利用交换图两条路径的等价性,将线性映射的像与核结构问题直接转化为矩阵的结构问题,使抽象的问题直观化,为研究像与核问题提供一种新的思维方式。

The concepts of image and core of linear mapping are abstract.So students are difficult to understand the structure.In current teaching materials,there is little discussion of Kerφand Imφ.So it is suggested to introduce interchange graph into the teaching materials,use equivalence property of the two pathways of interchange graph,transform the problem of image and core of linear mapping into matric structure problems,and make the abstract problems visualized,to provide a new thinking path of researching image and core problems.