Questions tagged [exterior-algebra]

It is a quotient - of the tensor algebra, obtained by taking graded sum over whole numbers $n$ of $n$-fold tensor products - by the ideal generated by elements of the form $a\otimes a$. We write the residue class of $a\otimes b$ in this algebra, as $a\wedge b$ and call it the wedge product.

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Equivalence of wedge and tensor product with Levi-Civita symbol

In this answer the following is stated: \begin{eqnarray} v\land w & = & \frac{1}{2!}(v\land w-w\land v) \\ & = & \frac{1}{2!}\epsilon_{\mu\nu}v^{\mu}\land w^{\nu} \\ & = & \...