What is wedgegeneral? — Mathematics

Definition 21.5 University Mathematics — Year 3 · Chapter 21 — Differential Forms and Stokes’ Theorem

The exterior product extends to a bilinear map $\Lambda^kE^* \times \Lambda^\ell E^* \to \Lambda^{k+\ell}E^*$ , determined by bilinearity and $(e_I^*) \wedge (e_J^*) = e_I^* \wedge e_J^*$ (concatenate and reorder; the product is $0$ if $I \cap J \neq \varnothing$ ). It is associative, and graded-anticommutative:

\beta \wedge \alpha = (-1)^{k\ell}\,\alpha \wedge \beta \qquad (\alpha \in \Lambda^k, \ \beta \in \Lambda^\ell).

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