[1]程明熙.二项式系数的矩阵表示及算法[J].东南大学学报(自然科学版),1983,13(4):106-114.[doi:10.3969/j.issn.1001-0505.1983.04.011]
 Cheng Ming-xi.Matrix Representation and its Algorithm of the Binomial Coefficients[J].Journal of Southeast University (Natural Science Edition),1983,13(4):106-114.[doi:10.3969/j.issn.1001-0505.1983.04.011]
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二项式系数的矩阵表示及算法()
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《东南大学学报(自然科学版)》[ISSN:1001-0505/CN:32-1178/N]

卷:
13
期数:
1983年第4期
页码:
106-114
栏目:
本刊信息
出版日期:
1983-12-20

文章信息/Info

Title:
Matrix Representation and its Algorithm of the Binomial Coefficients
作者:
程明熙
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Author(s):
Cheng Ming-xi
关键词:
二项式系数 矩阵表示 二项式定理 双线性变换 展开式 算法 控制理论 杨辉三角形 滑动平均法 传递函数
分类号:
+
DOI:
10.3969/j.issn.1001-0505.1983.04.011
摘要:
我国南宋时期(1261年)数学家杨辉曾将二项式系数表示成“杨辉三角形”。著名数学家牛顿最早证明了二项式定理。至今,二项式系数一般用组合表示。本文讨论了二项式系数和二项式定理的矩阵表示。这种表示法适宜于计算机上计算。二项式系数的应用较广泛,如,二项式系数的加权滑动平均、控制理论中的双线性变换等等。所以,二项式系数的矩阵表示是有意义的。
Abstract:
Binomial coefficients were expressed as "Yang Hui Triangle" by a Chinese mathematician Yang Hui in the Southern Song Dynasty (1261). The famous mathematician Newton first proved the binomial theorem. Up to now, binomial coefficients are generally represented by combinations. In this paper, we discuss matrix representation of the binomial coefficients and the binomial theorem. This representation is convenient for calculation on computer. The application of the binomial coefficients is quite extensive, for example, it may be used in weighted moving average method of prediction, in bilinear transformation in control theory, and so on. Therefore, matrix representation of the binomial coefficients is meaningful.
更新日期/Last Update: 2013-05-01