Exterior Product

The Exterior Product is commonly called the Wedge Product.

The Exterior Product generalizes the cross product of 3-vectors.

Define vectors v and u to be

  • u = u^1e_1 + u^2e_2 + u^3e_3
  • v = v^1e_1 + v^2e_2 + v^3e_3

v \wedge u = (v^1u^2 - v^2u^1)(e_1 \wedge e_2) + (v^1u^3 - v^3u^1)(e_1 \wedge e_3) + (v^2u^3 - v^3u^2)(e_2 \wedge e_3)