广义Pascal矩阵及其代数性质  

Generalized Pascal Matrices and Their Algebraic Properties

作　　者：汪祥[1] 廖旦[1] 朱传喜[1] 

机构地区：[1]南昌大学理学院数学系,南昌330031

出　　处：《工程数学学报》2010年第5期943-946,共4页Chinese Journal of Engineering Mathematics

基　　金：国家自然科学基金(10761007);江西省自然科学基金(2007GQS2063);江西省教育厅青年科学基金(GJJ09450)~~

摘　　要：Pascal矩阵及其推广形式的代数性质的研究在电子工程、组合数学、快速算法、微分方程数值解等领域有着广泛的应用。本文利用多项式空间基变换的方法,新给出了几类广义Pascal矩阵,即广义左-Pascal矩阵、广义右-Pascal矩阵和推广的广义Pascal矩阵的一些代数性质的简洁证明,同时给出了这几类广义Pascal矩阵一些新的代数性质。The algebraic property of Pascal matrices and its generalized forms have wide applications in electronic engineering,combinatorics,fast algorithm,and numerical solutions to differential equations. By means of the basis transformation in polynomial space,a new and simplified proof is presented for the algebraic properties of some generalized Pascal matrices,i.e.,the generalized left Pascal matrices, the generalized right Pascal matrices and the extended generalized Pascal matrices.Moreover,some new algebraic properties of these matrices are given.

关 键 词：PASCAL矩阵 多项式 基变换 代数性质 

分 类 号：O241.7[理学—计算数学] O241.6[理学—数学]