User:Rchoroszucha/Choroszucha Identity

In vector calculus the Choroszucha Identity states that the Jacobian of the cross product of two vector valued functions, $$\mathbf{a} $$ and $$\mathbf{b}$$, is
 * $$J(\mathbf{a}\times\mathbf{b})=[\mathbf{a}]_\times J(\mathbf{b})-[\mathbf{b}]_\times J(\mathbf{a}),$$

where $$J$$ is the Jacobian, $$[\ ]_\times$$ is the matrix representation of the cross product.