通常高等代数教材中以排列逆序为基础定义n阶行列式的值并证明其性质。为简便,也有教材,特别许多工科教材中用归纳法(或称递推法)定义n阶行列式的值,如[1]、[2]等。但教材中对于这种定义缺少系统的叙述,对于其性质也未给出严格证明。本文拟就系统叙述行列式的这种定义,并由此证明其性质。 定义一 把1~2,2~2,…,n~2个数排成正方形数表,并在两旁画两道竖线 Usually higher algebra textbooks in order to arrange the reverse sequence based on the value of the n-order determinants and prove its nature. For simplicity, there are also textbooks. In particular, many engineering textbooks use inductive (or recursive) methods to define n-th determinant values, such as [1], [2], etc. However, there is a lack of systematic account of this definition in the textbooks and no strict proof of its nature. This article intends to describe this definition of determinant system, and thus prove its nature. Define a 1 ~ 2, 2 ~ 2, ..., n ~ 2 number into a square number table, and draw two vertical lines