The **Wedge product** is the multiplication operation in exterior algebra. The wedge product is always antisymmetric, associative, and anti-commutative. The result of the wedge product is known as a bivector; in (that is, three dimensions) it is a 2-form. For two vectors **u** and **v** in ℝ^{3}, the wedge product is defined as

where ⊗ denotes the outer product. Note that the bivector has only three indepedent elements; as such, it can be associated with another vector in ℝ^{3}. If the associated vector is defined as

it is the same as the cross product of **u** and **v**. In this sense, the cross product is a special case of the exterior product.

## Bivectors

- See also: Rotation_matrix#Rotation_matrix_from_axis_and_angle and Cross_product#Conversion_to_matrix_multiplication

Bivectors are commonly used to represent rotations.