grandes-ecoles 2014 QIIIB4

grandes-ecoles · France · centrale-maths1__pc Implicit equations and differentiation Differentiability proof and derivative formula for abstract/matrix-valued functions

Let $f$ be a function of class $C^2$ from $\mathbb{R}^n$ to itself. What is the necessary and sufficient condition on $f$ for the Jacobian matrix $J_f(x)$ to be antisymmetric for all $x$ in $\mathbb{R}^n$?

Let $f$ be a function of class $C^2$ from $\mathbb{R}^n$ to itself. What is the necessary and sufficient condition on $f$ for the Jacobian matrix $J_f(x)$ to be antisymmetric for all $x$ in $\mathbb{R}^n$?

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