Graduation Year

2005

Document Type

Thesis

Degree

M.A.

Degree Granting Department

Mathematics and Statistics

Major Professor

Brian Curtin, PhD.

Keywords

Linear algebra, Lucas numbers, Product identites, Asymptotics, Golden ratio

Abstract

By the n-th Fibonacci (respectively Lucas) vector of length m, we mean the vector whose components are the n-th through (n+m-1)-st Fibonacci (respectively Lucas) numbers. For arbitrary m, we express the dot product of any two Fibonacci vectors, any two Lucas vectors, and any Fibonacci vector and any Lucas vector in terms of the Fibonacci and Lucas numbers. We use these formulas to deduce a number of identities involving the Fibonacci and Lucas numbers.

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