For u and v in a vector space V, their exterior product is denoted u∧v and satisfies u∧v = −v∧u. If v₁, …, v_n form a basis for V, then v_i∧v_j, where i < j, form a basis for the exterior product ⋀²V. Further exterior product spaces ⋀^kV can be defined for 1≤ k ≤dimV.