Matrix algebra and geometric algebra are two different languages for many of the same topics/structures. If you like you can embed either one in the other (thou

Matrix algebra and geometric algebra are two different languages for many of the same topics/structures. If you like you can embed either one in the other (though embedding geometric algebra into matrix algebra is extremely cumbersome, sort of like rewriting your Python programs in assembly language). Geometric algebra has a much richer geometrical structure, but in some contexts the more basic structure of linear transformations is all you need, and matrices work just fine. In geometric algebra, you can extend a linear transformation of vectors by "outermorphism" to act on arbitrary multivectors.