Generalized Pascal functional matrix and its applications

被引：33

作者：

Yang, Yongzhi ^{[1
]}

Micek, Catherine ^{[1
]}

机构：

[1] Univ St Thomas, Dept Math, St Paul, MN 55105 USA

来源：

LINEAR ALGEBRA AND ITS APPLICATIONS | 2007年 / 423卷 / 2-3期

关键词：

generalized Pascal functional matrix; Pascal matrices; combinatorial identities; LU decomposition; generalizing functions;

D O I：

10.1016/j.laa.2006.12.014

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper, we introduce the generalized Pascal functional matrix and show that the existing variations of Pascal matrices are special cases of this generalization. We study some algebraic properties of such generalized Pascal functional matrices. In addition, we demonstrate a direct application of these properties by deriving several novel combinatorial identities and a nontraditional approach for LU decompositions of some well-known matrices (such as symmetric Pascal matrices). (C) 2007 Elsevier Inc. All rights reserved.

引用

页码：230 / 245

页数：16

共 10 条

[1] [Anonymous], MATH MAG
[2] Matrix approach to polynomials 2
Arponen, T
[J]. LINEAR ALGEBRA AND ITS APPLICATIONS, 2005, 394 : 257 - 276
[3] The linear algebra of the generalized Pascal functional matrix
Bayat, M
Teimoori, H
[J]. LINEAR ALGEBRA AND ITS APPLICATIONS, 1999, 295 (1-3) : 81 - 89
[4] BRAWER R, 1992, LINEAR ALGEBRA APPL, V174, P13, DOI 10.1016/0024-3795(92)90056-G
[5] PASCAL MATRICES
CALL, GS
VELLEMAN, DJ
[J]. AMERICAN MATHEMATICAL MONTHLY, 1993, 100 (04) : 372 - 376
[6] Stirling matrix via Pascal matrix
Cheon, GS
Kim, JS
[J]. LINEAR ALGEBRA AND ITS APPLICATIONS, 2001, 329 (1-3) : 49 - 59
[7] Roman S., 1984, Volume 111 of Pure and Applied Mathematics
[8] The factorization of block matrices with generalized geometric progression rows
Yang, YZ
Holtti, H
[J]. LINEAR ALGEBRA AND ITS APPLICATIONS, 2004, 387 : 51 - 67
[9] Zhang ZZ, 1998, LINEAR ALGEBRA APPL, V271, P169
[10] The algebraic properties of the generalized Pascal functional matrices associated with the exponential families
Zhao, XQ
Wang, TM
[J]. LINEAR ALGEBRA AND ITS APPLICATIONS, 2000, 318 (1-3) : 45 - 52

← 1 →