# 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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### Showing exterior product is skew-commutative

I am learning about the exterior product and wish to show the skew commutative property. Here is my work: I am confused on how to handle the notation of $(\omega^k \wedge \omega^l)$ as at the end I ...
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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} \\ & = & \...
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### Is there a difference between the wedge product and the exterior product?

I haven't been able to find much on the internet regarding this distinction (if there is one). I suspect they might be different, but I'm not sure.
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### Clifford algebra and exterior algebra

Let $E$ be a finite dimensional real vector space with $E^*$ its dual, and let $\langle \; , \; \rangle$ be an inner product on $E$. For any $e \in E$, denote by $e^* = \langle e, \; \rangle \in E^*$ ...
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### $\ell_1$ norm of multivector in exterior algebra

Suppose you have a set of $n$ linearly independent vectors $v_1, v_2, ..., v_n$. Then we can call their wedge product $W = v_1 \wedge v_2 \wedge ... \wedge v_n$. The $\ell_2$ norm $\|W\|_2$ is equal ...
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### What “cross products” do I need to find the volume of a cuboid?

In two dimensions, one can find the area for a quadrilateral by calculating two "cross products". If the vertices of the quadrilateral are $a, b, c, d$ clock-wise, consider the vectors $A = \vec{ab}$,...
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