Graduation Year
2005
Document Type
Thesis
Degree
M.A.
Degree Granting Department
Mathematics and Statistics
Major Professor
Brian Curtin, PhD.
Committee Member
Thomas Bieske, PhD.
Committee Member
David Stone, 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.
Scholar Commons Citation
Salter, Ena, "Fibonacci Vectors" (2005). USF Tampa Graduate Theses and Dissertations.
https://digitalcommons.usf.edu/etd/841
