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.
| Identifer | oai:union.ndltd.org:USF/oai:scholarcommons.usf.edu:etd-1840 |
| Date | 20 July 2005 |
| Creators | Salter, Ena |
| Publisher | Scholar Commons |
| Source Sets | University of South Flordia |
| Detected Language | English |
| Type | text |
| Format | application/pdf |
| Source | Graduate Theses and Dissertations |
| Rights | default |
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