Wedge Product

$u \wedge v = u \otimes v - v \otimes u$

The symbol $\otimes$ designates an Outer Product.

$u \wedge v = \begin{bmatrix} u_1\overline{v_1} - v_1\overline{u_1} & u_1\overline{v_2} - v_1\overline{u_2} & u_1\overline{v_3} - v_1\overline{u_3} \\u_2\overline{v_1} - v_2\overline{u_1} & u_2\overline{v_2} - v_2\overline{u_2} & u_2\overline{v_3} - v_2\overline{u_3} \\u_3\overline{v_1} - v_3\overline{u_1} & u_3\overline{v_2} - v_3\overline{u_2} & u_3\overline{v_3} - v_3\overline{u_3} \end{bmatrix}$

The wedge product of two vectors in ℝ³ gives the area of parallelogram they enclose.

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