# Tag Info

There are two relationships along these lines. The one you are referring to, I think, is the linear isomorphism between a Clifford algebra of $(V,Q)$ and the exterior algebra for $V$ mentioned in the wiki article. This lets you apply some intuition from exterior algebra inside the Clifford algebra. This linear isomorphism lets you identify a linear copy of ...
Well, actually the perspective should be reversed. Starting from the geometric product $a b$ having an inverse as mentioned $$a a^{-1}=1$$ one can define 2 identities $$a \cdot b= \frac{1}{2} \left(a b + \alpha(a) \, \alpha (b) \right)$$ where $\alpha$ is the reflection automorphism  a \wedge b= \frac{1}{2} \left(a b - \alpha(a) \, \alpha (b) \...