Geometric algebra contains operations to determine the union and intersection of subspaces, the join and meet products.

These products are of course important in geometry, and it is therefore disappointing to learn that they are not very tidy algebraically. In particular, they are not (bi-)linear: a small disturbance in their arguments may lead to major changes in their outcome as geometric degeneracies occur. This will give their treatment a different flavor than the products we introduced so far.

But meet and join are still very useful. Even when applied to the subspaces at the origin, meet and join generalize some specific formulas from 3-D linear algebra into a more unified framework and extend them to ...

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