The vector product on a firm foundation

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Abstract
It is so easy to define, use and explain the vector product of two vectors in three‐dimensional space, but without any clear idea regarding the underlying nature of the algebra involved in its definition and properties. This paper seeks to gather up its definition, properties and generalization to a space of n dimensions, using the necessary concept of rotation of rectangular axes in such a space. The subject is first examined using matrix notation, such an examination being necessarily restricted but useful in many applications. Suffix notation is later employed as a tool when the subject is developed using tensor theory. The generalization is only useful when the so‐called ‘ triple products ‘ emerge naturally in the theory. The author has found it helpful to have this background information available over the years, since it is not easily obtainable from standard textbooks on vector and tensor theory.

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