The title says it all but for some context:
In robotics the Jacobian maps a robot's joint velocities to the velocities at its end-point.
In some quadratic programming approaches (again in the robotics context) the Hessian is considered as $\mathbf{H}=J^TJ$. Note that in our field often $J\in\mathbb{R}^{m\times n}, n > m$.
My question is, under what conditions $\mathbf{H}=J^TJ$ holds or is a valid approximation. I've seen papers that say this notion isn't valid in some cases.
