exterior product

The wedge product is the product in an exterior algebra. If α and β are differential k-forms of degrees p and q, respectively, then α⋀β = (-1)^(p q) β⋀α. It is not (in general) commutative, but it is associative, (α⋀β)⋀u = α⋀(β⋀u), and bilinear (c_1 α_1 + c_2 α_2)⋀β = c_1(α_1 ⋀β) + c_2(α_2 ⋀β) α⋀(c_1 β_1 + c_2 β_2) = c_1(α⋀β_1) + c_2(α⋀β_2) (Spivak 1999, p. 203), where c_1 and c_2 are constants.

cup product | determinant | differential k-form | exterior algebra | exterior derivative | exterior power | inner product | module tensor product | vector space | volume | volume element