We can denote the jacobian of a vector map ##\pmb{g}(\pmb{x})## by ##\nabla \pmb{g}##, and we can denote its determinant by ##D \pmb{g}##. We were asked to prove that

##\sum_j \frac{\partial ~ {cof}(D \pmb{g})_{ij}}{\partial x_j} = 0##

generally holds so long as the ##g_i## are suitably differentiable not too long ago. Looking around, this property is mentioned in passing in papers here and there. Does this result go by a headword that I can look up. Like a theorem name of some sort? It is rumored to be an essential property for things like degree theory and the brouwer fixed point theorem.

##\sum_j \frac{\partial ~ {cof}(D \pmb{g})_{ij}}{\partial x_j} = 0##

generally holds so long as the ##g_i## are suitably differentiable not too long ago. Looking around, this property is mentioned in passing in papers here and there. Does this result go by a headword that I can look up. Like a theorem name of some sort? It is rumored to be an essential property for things like degree theory and the brouwer fixed point theorem.

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