\[ \mathbf{V}_1 \times \mathbf{V}_2 = \begin{vmatrix} \mathbf{i} & \mathbf{j} & \mathbf{k} \\ \frac{\partial X}{\partial u} & \frac{\partial Y}{\partial u} & 0 \\ \frac{\partial X}{\partial v} & \frac{\partial Y}{\partial v} & 0 \\ \end{vmatrix} \]

多行对齐：

\[ \begin{gather} \begin{split} Adv^{Fed} & = Pr^{Fed}\left ( A=1\mid x\in D_{T} \right ) - Pr^{Fed}\left ( A=1\mid x\in D_{N} \right ) \\ & = \underset{x\in D_{T}}{E^{Fed}}\left ( P\left ( A=1\mid x \right ) \right )-\underset{x\in D_{N}}{E^{Fed}}\left ( P\left ( A=1\mid x \right ) \right ) \\ & = \underset{x\in D_{T}}{E^{Fed}}\left ( 1-\frac{L\left ( \left ( x,y \right ),F \right )}{A} \right )-\underset{x\in D_{N}}{E^{Fed}}\left ( 1-\frac{L\left ( \left ( x,y \right ),F \right )}{A} \right )\\ & = \frac{1}{A}\cdot \left [ \underset{x\in D_{N}}{E^{Fed}}\left ( L\left ( \left ( x,y \right ),F \right )\right )-\underset{x\in D_{T}}{E^{Fed}}\left ( L\left ( \left ( x,y \right ),F \right ) \right ) \right ] \\ \end{split} \end{gather} \]