用递归关系计算n阶行列式的规律

Some Rules for Evaluating Determinants of Order n by Recursion Relations

给出了用递归关系方法求任意ｎ阶行列式的值的一般方法：首先，把已知的ｎ阶行列式看作为阶数ｎ的一个函数，记为Ｄ（ｎ）；其次，按行或按列展开这个行列式，并仔细观察存在于余子式及Ｄ（ｎ）里的关系，建立关于Ｄ（ｎ）的某一递归关系，此关系总为一个齐次的或非齐次的递归关系；最后。借助于Ｄ（０）、Ｄ（１）和Ｄ（２）等求出递归关系的通解的系数．虽然此法不一定简单，但毕竟是一个有用的方法．

This paper put forward a general method for finding the value of any determinant of order n by means of recursion. First, the determinant is regarded as a function of order n and denoted by D(n); Second, the determinant is expanded by row or by column, thenthe relation in both of D(n) and subdeterminants will be examined in details to set up certaina recursion, generally speaking, it must be a homogenous or a nonhomogenous recursion; finally the coefficients of the general solution are found out with the aid of D(0), D(1) andD(2) and so on. The method may not be simple, yet useful and effective.