Elements of the Homometric Vector K-Product Part I
- Author Francisco Zau
- DOI http://wwj
- Country : Angola
- Subject :
Keywords : Vector product, homometric k-product, n-dimensional vector spaces
Abstract
This paper aims to generalize the usual vector product between two given vectors, defined by Gibbs and Heaviside, from three-space to n-space. Next, although not very intuitive, this idea will be generalized to define an axial vector simultaneously orthogonal to any k given vectors of an n-dimensional vector space H^n, with 2≤k∈N, considering the orthogonality condition defined by the usual scalar product. The vector product thus generalized is given the name homometric vector k-product, because an axial vector of H^n, whose components are solutions of a homogeneous linear system of k equations with n unknowns, results from this product. For this first part, some specific properties of the homometric vector product will be analyzed, highlighting the high theoretical and practical value of this operation for science and engineering.
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