Assistant teaching of linear algebra based on geometric interpretation and practical application

Abstract

Linear algebra is not only a powerful tool in dealing with the problem of multi-variables, but also strongly logical. Students always feel that linear algebra is abstract, boring, and difficult to understand. For the teaching of linear algebra, the instructional design of linear algebra that combining the geometry intuition and practical application is proposed to help students understand the abstract knowledge. As an example in our teaching process, the geometric interpretation of matrix, similar matrices, eigenvalues and eigenvectors are given in turn. This teaching method aims to help students shift perception from visual to abstract and thus improve the teaching efficiency of linear algebra. The practical application of eigenvalue in image compression, i.e. Karhunen-Loeve transform, is presented. It is advantages to promote students' motivation in learning and cultivate their abilities in using mathematics to solve practical problems.