逆矩阵的判定及计算方法

Criteria and Computations for Matrix Inverse

线性代数是大学教育中一门难度较高的基础必修课程,而逆矩阵是教学过程中一个主要概念,对研究其他线性结构有着非常重要的作用.本文通过对逆矩阵定义的分析,汇总若干个判定矩阵是否可逆的方法,同时提供了多种逆矩阵的计算技巧,包括利用计算机技术简化繁琐的计算过程,这些都是学习者在学习过程中需要掌握的重要内容.本文旨在协助教师在开展教学时,能够举一反三,以点带面来引导学生将所学知识融合,注重知识点之间的相关性学习;同时,也帮助学习者能够更加全面的认识逆矩阵这一重要概念.

In higher education, Linear Algebra is a fundamental course which is quite challenging to many learners. The invertibility of a matrix is a key concept in the teaching and learning process, which plays a very important role in the study of other structures of linear algebra as well. In this article, we analyze the definition of the invertible matrix and summarize several methods for determining and computing the inverse of an invertible matrix, including the use of different software to simplify complicated calculation processes. These are an important part of contents of Linear Algebra for learners to acquire. The aim of this article is to assist teaching by inferring other things from one fact in the teaching process, and by paying attention to the correlation among different concepts. At the same time, we are also hoping to help the learners to understand the important concept of the invertible matrices.