Date:  2024-05-21

Article ID:  81674

This article uses the question in the title to motivate the wedge product, also called the exterior 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.