On Fibonacci Vectors

Abstract

The purpose of this article is to study vector products of Fibonacci 3-vectors, Fibonacci 4-vectors and Fibonacci 7-vectors. To achieve this, we first describe the corresponding anti-symmetric matrix for the Fibonacci 3-vector and reconsider the vector product with the aid of this matrix. We examine certain properties of this vector product. Furthermore, we define vector products for Fibonacci 4-vectors and Fibonacci 7-vectors. We also give in the same vein the corresponding anti-symmetric matrix for Fibonacci 7-vector and redefine the vector product by using this matrix. In the final instance we investigate the Lorentzian inner products, Lorentzian vector products and Lorentzian triple scalar products for Fibonacci 3-vectors, Fibonacci 4-vectors and Fibonacci 7-vectors.