10 THE VECTOR SPACE MODEL: THE ALGEBRA OF DIRECTIONS

When we developed geometric algebra in the first part of this book, we illustrated the principles with pictures in which vectors are represented as arrows at the origin, bivectors as area elements at the origin, and so on. This is the purest way to show the geometric properties corresponding to the algebra.

The examples showed that you can already use this algebra of the mathematical vector space image to model useful aspects of Euclidean geometry, for it is the algebra of directions of n-dimensional Euclidean space. We explore some more properties of this model in this chapter, with special emphasis ...

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