Before Start
This is just a test post! 
Basic Fomula
Given a mapping: $f: R^N \rightarrow R^M$ and input X with dimension N, output with dimension M, we we call the matrix with following form a Jocobian Matrix:
\[\frac{\partial{y}}{\partial{x}} = \begin{bmatrix} \frac{\partial{y_1}}{\partial{x_1}} & \frac{\partial{y_1}}{\partial{x_2}} & \cdots & \frac{\partial{y_1}}{\partial{x_N}} \\ \frac{\partial{y_2}}{\partial{x_1}} & \frac{\partial{y_2}}{\partial{x_2}} & \cdots & \frac{\partial{y_2}}{\partial{x_N}} \\ \vdots & \vdots & \ddots & \vdots \\ \frac{\partial{y_M}}{\partial{x_1}} & \frac{\partial{y_M}}{\partial{x_2}} & \cdots & \frac{\partial{y_M}}{\partial{x_N}} \\ \end{bmatrix}\]
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