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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 ...


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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) \...



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