Sherman-Morrison公式的五种证明方法

Five Proof Methods for the Sherman-Morrison Formula

摘要: 本文分别用矩阵分解、矩阵的升阶运算、矩阵的初等变换、矩阵方程的求解以及因式分解的方法，给出了Sherman-Morrison公式的五种证明方法，更加明确了Sherman-Morrison公式的构造过程，丰富了高等代数课程教学内容。通过在一题多解的课堂教学中采用针对性的措施活跃学生的解题思维，进一步提高学生的解题能力。

Abstract: This paper provides five proof methods for the Sherman-Morrison formula by using matrix decom-position, ascending order method, matrix elementary transformation, the solution of matrix equa-tions, and factorization methods. Those clarify the construction process of the Sherman-Morrison formula, enrich the teaching content of the course. By adopting targeted measures in classroom teaching with multiple solutions to one problem, students can activate their problem-solving think-ing and further improve their problem-solving abilities.