一类含参行列式的思考

Consideration on a Type of Determinants with Parameters

本文给出了一种简化一类n阶行列式计算的参数方法.先通过引入参数t_i(i≤n),构造参数t_i(i≤n)的行列式,且从理论上证明了它是关于t_i(i≤n)的线性函数;再通过待定系数法,确定这个线性函数,从而得到关于参数t_i(i≤n)的行列式值,进而求得所要计算的行列式;最后,利用此式还给出了求行列式的代数余子式之和的简洁计算方法.

This paper presents a parameters method for calculating a type of determinants. Firstly,a deter- minant with parameters ti （i≤n） is introduced, whose determinant is proved to be a linear function of ti（i≤n）. Secondly, the linear function can be determined by the method of undetermined coefficients. Therefore the determinant with （or without） parameters ti （i≤n） is evaluated. We also have a short approach to the calculation of the sum of the cofactors of a determinant.