关于用伴随矩阵求逆阵的推导——教学札记

• 作 者: 罗崇萐
• 出 处: 数学通报
• 发表日期: 1983年03期
• 关键词: 伴随矩阵 逆阵 初等变换 非奇异矩阵 线性组合 余子式 求逆 学生思维能力 认识规律 行向量

(一) 用伴随矩阵求逆阵的公式的推导,一般书上都是先给出矩阵A的伴随矩阵A~*,再证AA~*=|A|I,然后指出:当|A|(?)0时,A(1/|A|A~*)=I,从而有A~(-1)=1/|A| A~*。这样的推导,理论上固然很严谨,方法上看来也简捷,但是,陡然提出伴随矩阵,似乎不合认识规律,无益于学生思维能力的发展。

(1) Using the derivation of the adjoint matrix to derive the inverse matrix formula, the general book first gives the adjoint matrix A~* of the matrix A, and then proves that AA~*=|A|I, and then states: When |A| ( When 0), A(1/|A|A~*)=I, so that A~(-1)=1/|A|A~*. Such derivation is theoretically very rigorous and simple in terms of method. However, suddenly the adjoint matrix is ​​proposed, which does not seem to fit the law of understanding and does not benefit the development of students’ thinking ability.