English: Relations between multivectors in geometric algebra. This diagram neglects some details, especially not expressing subsets and intersections. For example, all r-blades are r-vectors, and they are all multivectors. In addition, 0 is both a scalar and a vector, as well as all kinds of r-blades. Also in dimensions below four, there is no distinction between blades and vectors, because all r-vectors are actually r-blades. Another detail is the requirements for vectors in the products. Specifically, vectors for a versor need to be invertible.
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