I've read somewhere the following identity for a tensor rank 2
$ \nabla \times \nabla v =0 $
where $v$ is a vector of "j" components and $\nabla = \frac{\partial}{\partial x_i}$, such that $ \nabla v $ forms a tensor rank 2.
First off, is this true? Second, what if $v$ was replaced with a tensor of rank n? (I'm assuming you can take the gradient of any tensor rank, true?)