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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 ℝ3 it is a 2-form. For two vectors u and v in ℝ3, 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 ℝ3. If the associated vector is defined as

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  • Wedge product
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  • 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 ℝ3 it is a 2-form. For two vectors u and v in ℝ3, 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 ℝ3. If the associated vector is defined as
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abstract
  • 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 ℝ3 it is a 2-form. For two vectors u and v in ℝ3, 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 ℝ3. 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.
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