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I have a function $ f:\Re^2\to\Re^2$ and would like to understand why $ |Jf(x)|=\max_\theta|D_\theta f(x)|\cdot\min_\theta|D_\theta f(x)|$ , that is, why the determinant of the Jacobian of $ f$ at $ x$ is equal to the product of min and max of the directional derivatives at $ x$ . I think it must be a moreRead more