The Jacobian matrix of a vector valued function $f$ can be denoted $$J(f(x))$$
where each element of this matrix is given as $$J_{ij}(f(x))$$
Does anyone know good way of denoting the row or the column of the Jacobian matrix? For example, is it common to denote the $i$th row as $[J(f(x))]_i$?
The $(i,k)$ entry of the Jacobian at $x$ is $${\partial f_i\over\partial x_k}(x)\ .\tag{1}$$ The $i^{\rm th}$ row of the Jacobian is then given by $$\left({\partial f_i\over\partial x_1},{\partial f_i\over\partial x_2},\ldots,{\partial f_i\over\partial x_n}\right)_x=\nabla f_i(x)\ .$$ The $k^{\rm th}$ column of the Jacobian contains the partial derivatives of the $m$ components $f_i$ of $f$ with respect to the $k^{\rm th}$ variable. There is no standard notation for such a column. In any case $$J_f(x)\,e_k$$ or $${\partial f\over\partial x_k}$$ are correct, albeit typographically somewhat clumsy. I usually write $f_{i.k}(x)$ for the partial derivative $(1)$ and $f_{.k}(x)$ for said column vector, omitting the $(x)$ when appropriate.