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.

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