行列式的归纳定义及其性质的证明

The Definition of n-Order Determinants by Mathematical Induction and Proof of Its Properties

在不同的代数教材中给出了行列式的不同定义,一般教材中n阶行列式的古典定义,学生学习起来比较困难,有些教材采用归纳法定义n阶行列式,但是行列式性质的证明却很复杂,不得不把证明放入附录中。为了使学生学习起来比较顺畅,采用归纳法定义n阶行列式,利用全新的方法给出了n阶行列式性质的简单证明,并给出了n阶行列式的古典定义与归纳法定义的等价性的证明。

Different forms of the definition of determinant are given in various linear algebra textbooks. The traditional definition is difficult for students to understand. Although the definition defined by induction is easier to understand, the proof of the determinant properties stemming from this kind of definition is complicated. As a result, the complicated proof can only be put in the appendix. In order to make it easier to be understand, the definition of determinant is given by induction, and the properties of determinant of order n proved by a new method and the equivalence of the traditional definition of determinant as well as the definition by induction also proved.