Definition:Jacobian

Definition
Let $U$ be an open subset of $\R^n$.

Let $\mathbf f = \left({f_1, f_2, \ldots, f_m}\right)^\intercal: U \to \R^m$ be a vector valued function, differentiable at $\mathbf x = \left({x_1, x_2, \ldots, x_n}\right)^\intercal \in U$.

Also known as
Note that both concepts are often called just the Jacobian of $\mathbf f$ at $\mathbf x$.

It is advisable to use the full term for whichever is intended unless context makes it obvious which one is meant.