n阶r-循环行列式的计算及其应用

Calculation for nth Order r-Recurrent Determinant and Its Application

文章首先给出n阶r-循环矩阵及其行列式的定义;然后,分别用析因子法、作辅助行列式法及特征根法证明了n阶r-循环行列式的计算公式|D|=∏nk=1f(xk);最后,给出该公式在两个方面的应用:(1)用来计算具有某些特征的行列式的值;(2)可以推出一些有关多项式的有趣结论.

First this paper defines the nth order r- Recurrent matice and r- Recurrent determinant; then the n formula D = nⅡk=1 f（xk） of nth order r - recurrent determinant is proved by the following three methods： Factor analysis method, determinant for auxiliary method and characteristic root method; At last, applications of the n formula D =nⅡk=1 f（xk） are given： calculating some special deteminants and deducing some interesting results about Polynomial theory.