Wedge product

The antisymmetric product that builds higher-degree forms: $\alpha\wedge\beta = -\beta\wedge\alpha$ .

The wedge product $\wedge$ combines two forms into a higher-degree form, antisymmetrically: $\alpha\wedge\beta=-\beta\wedge\alpha$ , so $\alpha\wedge\alpha=0$ for any 1-form $\alpha$ . Geometrically, $dx\wedge dy$ measures signed area the way $dx$ alone measures signed length.

Examples

$dx\wedge dy = -dy\wedge dx$ , and $dx\wedge dx = 0$ .