Factored matrices can generate combinatorial identities

By identifying the terms in the LU decomposition of various matrices, one produces combinatorial identities. Examples are given with formulas involving binomial coefficients and other numbers arising from simple recurrence formulas, number-theoretic functions, q-series, and orthogonal polynomials.

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Bibliographic Details
Published in:	Linear algebra and its applications Vol. 438; no. 4; pp. 1667 - 1677
Main Author:	Chamberland, Marc
Format:	Journal Article
Language:	English
Published:	Elsevier Inc 15-02-2013
Subjects:	Fibonacci numbers Matrix factorization Stirling numbers of the second kind Fibonacci numbers Stirling numbers of the second kind Matrix factorization
Online Access:	Get full text
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Description
Summary:	By identifying the terms in the LU decomposition of various matrices, one produces combinatorial identities. Examples are given with formulas involving binomial coefficients and other numbers arising from simple recurrence formulas, number-theoretic functions, q-series, and orthogonal polynomials.
ISSN:	0024-3795 1873-1856
DOI:	10.1016/j.laa.2011.08.030