Hello! in Little Spivak, p. 79, we find this:

We will therefore define a new product, the

wedgeproduct $\omega\wedge\eta\in > \Lambda^{k+\ell}(V)$ by $$ > \omega\wedge\eta = > \frac{(k+\ell)!}{k!\ell!}\mathrm{Alt}(\omega\otimes\eta). > $$

It is ambiguous whether Spivak means for this to be defined for all $\omega\in\mathcal{J}^k(V),\eta\in\mathcal{J}^{\ell}(V)$ or only for $\omega\in\Lambda^k(V),\eta\in\Lambda^{\ell}(V)$. ($\mathcal{J}^n(V)$ is the set of $n$-tensors over vector space $V$, $\Lambda^n(V)$ is the set of alternating $n$-tensors over $V$.) Certainly the definition would make sense either way.

Which one is it?

In short: Is the wedge product applied to general tensors, or only to tensors which are already antisymmetric?