Category:Definitions/Jacobian Matrices

This category contains definitions related to Jacobian Matrices.
Related results can be found in Category:Jacobian Matrices.

The Jacobian matrix of $\mathbf f$ at $\mathbf x$ is defined to be the matrix of partial derivatives:

$\quad \mathbf J_{\mathbf f} := \begin{pmatrix} \map {\dfrac {\partial f_1} {\partial x_1} } {\mathbf x} & \cdots & \map {\dfrac {\partial f_1} {\partial x_n} } {\mathbf x} \\ \vdots & \ddots & \vdots \\ \map {\dfrac {\partial f_m} {\partial x_1} } {\mathbf x} & \cdots & \map {\dfrac {\partial f_m} {\partial x_n} } {\mathbf x} \end{pmatrix}$