摘要
该文以友矩阵的特征值为基础,讨论了形如“Pn(x)=xn-a1xn-1-a2xn-2-…-an-1x-an”的代数多项式的友矩阵的一些简单性质,并给出了组合恒等式的几个通项公式以及形如“S(n)=a.S(n-1)+b.S(n-2)+c.S(n-3)”的递归数列的通项公式.
In this paper the author discusses the simple properties of companion matrix of algebraic polynomial "Pn(x)=x^n-a1x&n-1-a2x&n-2-...-an-1x-an", and gives some general formulas of combinatorial identity and recurrent sequence such as "S(n)=a·S(n-1)+b·S(n-2)+c·S(n-3)" by using the eigenvalues of the matrix.
出处
《甘肃联合大学学报(自然科学版)》
2005年第4期6-8,17,共4页
Journal of Gansu Lianhe University :Natural Sciences
关键词
代数多项式
友矩阵
组合恒等式
递归数列
algebraic poynomial
companion matrix
combinatorial identity
recurrent sequence