20 THE LINEAR PRODUCTS AND OPERATIONS

The linear products we use in this book are the geometric product, the outer product, the contraction inner products, the scalar product, and the commutator product. They are all linear in their arguments. Examples of unary linear operations that are discussed in this chapter are addition, reversion, grade involution, and grade extraction of multivectors. This chapter presents two ways to implement the linear products and operations of geometric algebra.

Both implementation approaches are based on the linearity and distributivity of these products and operations. The first approach uses linear algebra to encode the multiplying element as a square matrix acting on the multiplied element, which is encoded ...

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