两类下三角形Pascal矩阵的相似性  

ON THE SIMILARITY OF TWO KINDS OF LOWER TRIANGULAR PASCAL TYPE MATRICES

作　　者：杨胜良[1] 

机构地区：[1]兰州理工大学应用数学系,甘肃兰州730050

出　　处：《数学杂志》2011年第1期75-80,共6页Journal of Mathematics

基　　金：甘肃省自然科学基金资助项目(3ZS041-A25-007)

摘　　要：本文研究了Pascal矩阵与位移Pascal矩阵之间的关系.利用组合恒等式与矩阵分解的方法,得到了Pascal矩阵以及位移Pascal矩阵与若当标准型之间的过渡矩阵.同时也得到了这两类矩阵在域Zp上的最小多项式.This article investigates the connection between the lower triangular Pascal matrix and shifted Pascal matrix. By using combinatorial indentities and factorization of matrices, we show that the Pascal matrix and shifted Pascal matrix are similar to each other. Transition matrices between these two kinds of matrices and their Jordan canonical forms are found, and the minimal polynomials for the matrices over the field Zp are also obtained.

关 键 词：PASCAL矩阵 位移Pascal矩阵 STIRLING数 Stirling矩阵 若当标准型 

分 类 号：O157.1[理学—数学]