Date: 2023-05-08 | Article ID: 03910 |

This article introduces **Clifford algebra**, an associative algebra generated by vectors. Like the exterior algebra (article 81674), it includes objects representing k-dimensional subspaces for every k. Unlike the exterior algebra, though, Clifford algebra includes a scalar product of two vectors, like the one defined by the metric tensor at a given point in spacetime. For this reason, Clifford algebra is sometimes also called **geometric algebra**.

**2023-05-08**(added a phrase to clarify one definition, added a footnote about another isomorphism, added a warning about an error (a mis-typed equation) in one reference)**2023-04-30**(added note about a sign convention, with a reference)**2023-04-21**(first version)

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