Abstract
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 that have been introduced so far in the book. However, meet and join algorithm are still very useful. Even when applied to the subspaces at the origin, meet and join algorithm generalize some specific formulas from 3-D linear algebra into a more unified framework and extend them to subspaces intersecting in n-dimensional space. Their full power will be unleashed later, in Part II, when they can be used to intersect offset subspaces and even spheres, circles, and the like. Yet it is good to understand their algebraic structure first, and now all the tools to do so have been discussed.
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