|
Pure Mathematics 2024
Sherman-Morrison公式的五种证明方法
|
Abstract:
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。
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.
[1] | 尹小艳. 从一道课本例题谈矩阵求逆[J]. 高等数学研究, 2023, 26(5): 17-20. |
[2] | 陈建华, 焦荣政. 三对角矩阵求逆问题的思考——从一道课本习题谈起[J]. 大学数学, 2020, 36(1): 104-109. |
[3] | 李亭亭. 初等变换法求逆矩阵在线性代数教学与解题中的应用[J]. 数学大世界(上旬), 2023(5): 59-61. |
[4] | 曾聃, 徐运阁. 矩阵的逆及秩的降阶方法[J]. 大学数学, 2019, 35(5): 117-121. |
[5] | 北京大学数学系前代数小组. 高等代数[M]. 第5版. 王萼芳, 石生明, 修订. 北京: 高等教育出版社, 2019. |
[6] | Gene, H.G. and Charles, F.V.L. (1996) Matrix Computations. Johns Hopkins University Press, New York, 58-59. |