Jacobian

The Jacobian is a generalization of the Gradient where we look at a continuously differentiable function $f:{\mathbb{R}}^n\to {\mathbb{R}}^m$.

$$\frac{\partial f}{\partial x}=\left[\begin{array}{ccc}\frac{\partial f_1}{\partial x_1}& \cdots & \frac{\partial f_1}{\partial x_n}\\ ⋮& \ddots & ⋮\\ \frac{\partial f_m}{\partial x_1}& \cdots & \frac{\partial f_m}{\partial x_n}\end{array}\right]$$

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