【摘要】 矩阵在数学和工程等多个领域具有广泛的应用.通常的线性代数课程中只介绍非常基本的矩阵知识,难以满足后续的需要.本文先系统地总结矩阵之间的等价、相似以及合同关系,在此基础上介绍几种重要的矩阵分解技巧,并从逆矩阵的概念过渡到广义逆矩阵,通过知识点之间的串联与类比,帮助学生加深对矩阵理论的理解.实践表明,这是打造线性代数"金课"的有效做法.更多还原

【Abstract】 Matrices have been widely applied to many fields such as mathematics and engineering. In general linear algebra course, only basic knowledge on matrices is introduced, which does not meet the follow-up requirements sufficiently. In this article, the equivalence, similarity and contractual relationships between matrices are systematically summarized. Based on this, several important techniques on decompositions of matrices are introduced. After recalling some basic knowledge of invertible matrices, the concept on generalized inverses of matrices is introduced. The connection and analogy among these knowledge points are helpful for students to deepen their understanding of matrix theory. Practice shows that this is an effective way to build the "golden course" of linear algebra.更多还原