Hello! I am reading so very introductory stuff on geometric algebra and at a point the author says that, as a rule for calculation geometric products, we have that ##e_{12..n}=e_1\wedge e_2 \wedge ...\wedge e_n = e_1e_2...e_n##, with ##e_i## the orthonormal basis of an n-dimensional space, and I am not sure I understand this. As far as I understood, the wedge product of 2 vectors, is just the cross product and we have ##e_1e_2=e_1 \cdot e_2 + e_1 \wedge e_2=e_1 \wedge e_2##, which makes sense as the dot product of 2 perpendicular vectors is 0. But for 3 vectors we would have ##e_1e_2e_3=(e_1 \wedge e_2)e_3=(e_1 \wedge e_2) \cdot e_3 + (e_1 \wedge e_2)\wedge e_3 = e_1 \wedge e_2 \wedge e_3##, which is not true in euclidian space. So can someone explain to me how does the rule the author mentioned, works? Thank you!(adsbygoogle = window.adsbygoogle || []).push({});

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# I Outer product in geometric algebra

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