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In vector calculus the Choroszucha Identity states that the Jacobian of the cross product of two vector valued functions, ${\displaystyle \mathbf {a} }$ and ${\displaystyle \mathbf {b} }$, is^[1]

${\displaystyle J(\mathbf {a} \times \mathbf {b} )=[\mathbf {a} ]_{\times }J(\mathbf {b} )-[\mathbf {b} ]_{\times }J(\mathbf {a} ),}$

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

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