摘要:行列式是高等代数课程里基本而重要的内容之一，在数学和现实生活中有着广泛的应用，懂得如何计算行列式显得尤为重要.本文简述行列式的定义及基本性质，介绍了利用行列式的性质计算、化三角形法、代数余子式法、加边法（升阶法）、范德蒙得行列式法等5种基本计算方法以及数学归纳法、递推法、利用矩阵特征值计算、拆项法、因式分解法等5种特殊计算方法。本文也介绍了行列式的实践应用。这些行列式的计算方法及其应用可以提高我们对行列式的认识，有利于把行列式的研究推向深入。

关键词：行列式；因式分解；化三角形法；解析几何

ABSTRACT:Determinant of higher algebra curriculum content of basic and important one in mathematics and real life has a wide range of applications, know how to calculate the determinant is very important. This paper describes the definition and basic properties of determinant, the determinant of the nature described by calculation of the triangle method, algebraic method, adding edge method (Ascending Order), Vandermonde determinant method of 5 basic calculation methods and mathematical induction, recursion, the use of eigenvalue calculation, the dissolution of entry method, such as the factorization method of 5 special calculation methods. This article also describes the determinant in analytic geometry, algebra theory is applied and engineering construction, the practical application of economic management. The determinant of the calculation method and its applications can improve our understanding of the determinant, to facilitate the determinant of research depth.

Key words: determinant; factorization; triangle method; analytic geometry.