2022-02-06   81674

Can the Cross Product be Generalized to Higher-Dimensional Space?

This article uses the question in the title to motivate the wedge product. Many things that are traditionally expressed using the cross product in three-dimensional space have natural generalizations to any number of dimensions when expressed in terms of the wedge product. The wedge product can also be used to define the determinant of a linear transformation. Basic properties of the determinant are obvious from this definition.

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www.cphysics.org updated 2022-09-25