| Pascal矩阵与Vandermonde矩阵的关系 |
| |
| 引用本文： | 杨胜良,游宏.Pascal矩阵与Vandermonde矩阵的关系[J].数学研究及应用,2006,26(1):33-39. |
| |
| 作者姓名： | 杨胜良 游宏 |
| |
| 作者单位： | 1. 兰州理工大学应用数学系,甘肃,兰州,730050
2. 哈尔滨工业大学数学系,黑龙江,哈尔滨,150001 |
| |
| 基金项目： | the NSF of Gansu Province of China (3ZS041-A25-007) |
| |
| 摘 要： | EI-Mikkawy M证明了对称Pascal矩阵Q_n和Vlandermonde矩阵V_n之间满足矩阵方程Q_n=T_nV_n,这里T_n是一个随机矩阵。本文证明了随机矩阵T_n能够分解成第一类Stirling矩阵和对角矩阵的乘积,得到了矩阵T_n的元素之间的递推关系,从而回答了EI-Mikkawy M的一个公开问题。同时得到了一些与Stirling数相关的组合恒等式。
|
| 关 键 词： | Stirling数 Stirling矩阵 vandermonde矩阵 Pascal矩阵 |
| 文章编号： | 1000-341X(2006)01-0033-07 |
| 收稿时间： | 03 30 2004 12:00AM |
| 修稿时间： | 2004年3月30日 |
On a Relationship between Pascal Matrix and Vandermonde Matrix |
| |
| YANG Sheng-liang and YOU Hong.On a Relationship between Pascal Matrix and Vandermonde Matrix[J].Journal of Mathematical Research with Applications,2006,26(1):33-39. |
| |
| Authors: | YANG Sheng-liang and YOU Hong |
| |
| Institution: | Dept. of Appl. Math., Lanzhou University of Technology, Gansu 730050, China;Dept. of Math., Harbin Institute of Technology, Heilongjiang 150001, China |
| |
| Abstract: | EI-Mikkawy M obtained that the symmetric Pascal matrix Q_n and the Vandermonde matrix V_n are connected by the equation Q_n = T_nV_n, where T_n is a stochastic matrix in. In this paper, a decomposition of the matrix T_n is given via the Stirling matrix of the first kind, and a recurrence relation of the elements of the matrix T_n is obtained, so an open problem proposed by EI-Mikkawy is solved. Some combinatorial identities are also given. |
| |
| Keywords: | Stirling number Stirling matrix Vandermonde matrix Pascal matrix |
| 本文献已被 CNKI 维普 万方数据 等数据库收录！ |
| 点击此处可从《数学研究及应用》浏览原始摘要信息 |
| 点击此处可从《数学研究及应用》下载免费的PDF全文 |
