A generalization of the vector product

Abstract

The vector product, often called the cross‐product, is well known in classical mechanics; it is generally assumed to be characteristic of three‐dimensional space. In this paper a vector product is defined on spaces of arbitrary dimension (excluding one‐dimensional spaces) and the definition is shown to coincide with that of the well‐known cross‐product in the case of three‐dimensional spaces; the generalization throws additional light on some of the properties of the classical vector product.