摘要
给出了线性代数中“det(AB) =detAdetB”的一个数学归纳法证明。其中只用到了行列式的三个基本性质与行列式依行展开定理以及矩阵乘积的定义 ,避免了初等矩阵、矩阵的初等变换。
The theorem “det (AB)= det A det B ”in linear algebra was proved by mathematical induction.In the proof,only the three fundamental properties of determinant,the expansion of a determinant along row,the definition of matrix multiplication were used.As a result,the use of excess theoretical knowledge and advanced techniques,such as elementary matrix,elementary transformation of matrix,partitioning of matrix and Laplace's theorem in the theory of determinant was avoided.
