aka exterior product

The wedge product $\wedge: \wedge^k V \times \wedge^l V \to \wedge^{k+1} V$ is defined for $\alpha \in \wedge^k V$ and $\beta \in \wedge^l V$ as

$\alpha \wedge \beta = \pi(\alpha \otimes \beta)$

where $\otimes$ is the Tensor product operation, and $\pi$ is a projection operator from a Tensor power to the corresponding Exterior power. See wave-notebook for definition.

See here

Tensor and wedge products are Functorial under Linear maps.

Can also extend wedge product to Vector bundles