= Grassmann change-of-variables formula
{c}
{title2=$D\eta=(\det S)^{-1}D\xi$}
For independent <Grassmann variables> and an invertible ordinary matrix $S$, the linear change $\eta=S\xi$ transforms the <Berezin integral> measure by the inverse <Jacobian determinant>. Indeed, the highest-degree monomial transforms by $\det S$, and coefficient extraction must undo that factor. For paired variables $\eta=S\xi$ and $\bar\eta=\bar\xi S^{-1}$ the two factors cancel. The order of odd variables and differentials fixes the overall sign and must be kept consistent.
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