行列式在数学中，是由解线性方程组产生的一种算式。[1]其定义域为nxn的矩阵A，取值为一个标量，写作det(A)或 | A | 。行列式可以看做是有向面积或体积的概念在一般的欧几里得空间中的推广。或者说，在 n维欧几里得空间中，行列式描述的是一个线性变换对“体积”所造成的影响。无论是在线性代数、多项式理论，还是在微积分学中（比如说换元积分法中），行列式作为基本的数学工具，都有着重要的应用。 行列式概念最早出现在解线性方程组的过程中。十七世纪晚期，关孝和与莱布尼茨的著作中已经使用行列式来确定线性方程组解的个数以及形式。十八世纪开始，行列式开始作为独立的数学概念被研究。十九世纪以后，行列式理论进一步得到发展和完善。矩阵概念的引入使得更多有关行列式的性质被发现，行列式在许多领域都逐渐显现出重要的意义和作用，出现了线性自同态和向量组的行列式的定义。-Determinant in mathematics, is a formula by solving linear equations. [1] defined domain nxn matrix A, the value of a scalar, writing det (A) or | A |. Determinant can be seen as to the promotion of the concept of area or volume in general Euclidean space. Or, in the n-dimensional Euclidean space, described the impact of a linear transformation of the "volume" determinant. Both linear algebra, polynomial theory or calculus (for example change element integral method), the determinant as the basic mathematical tools have important applications. Determinant concept first appeared in the process of solving linear equations. Determinant of the seventeenth century late SEKI and Leibniz s writings have been used to determine the number of solutions of linear equations as well as the form. 18th century, the determinant started as an independent mathematical concepts being studied. The 19th century onwards, the the determinant theory further development and improvement. Matrix concept makes mo