Is there a less cumbersome notation for the Jacobian of some multivariate functions? For instance, suppose I have $n$ multivariate functions of $n$ variables, $u_1(x_1,...,x_n),...,u_n(x_1,...,x_n)$. The partial derivative notations that can be used are
$$\frac{\partial u_k}{\partial x_j} \equiv u_{k_{x_j}}$$
both of which are rather cumbersome when there are $n^2$ of them to write. Is there a more compact notation for the Jacobian or is this all we've got?
I sometimes write $\mathbf{J}f(x)$ and leave it at that. That way I view the Jacobian as not just an object, but a sort of operator, akin to the derivative.