sudgylacmoe | The Commutative and Anticommutative Parts of the Geometric Product @sudgylacmoe | Uploaded February 2024 | Updated October 2024, 2 minutes ago.
Many people (including myself sadly) have described the inner and outer products as the commutative and anticommutative parts of the geometric product, but this is not true in general. In this short, I provide several counterexamples to this idea, showing that "commutative part" and "anticommutative part" are just not useful ideas in general.

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