 Because "W" is the derivative of an orthogonal transformation, the bilinear form

is skew-symmetric.Thus we can apply the fact of exterior algebra that there is a unique linear form formula_84 on formula_85 that

where formula_87 is the exterior product of formula_9 and formula_89.Taking the sharp "L" of "L" we get

Introducing formula_91, as the Hodge dual of "L", and applying the definition of the Hodge dual twice supposing that the preferred unit 3-vector is formula_92

where

by definition.