5Binary Operations
Eight elementary binary operations, as listed in the middle section of Table 5.1, are provided within the Clifford numerical suite. These are not all independent, and some can be defined in terms of others. The scalar multiplication returns the complex coefficient of the inner multiplication, with no unit 
attached. The interior derivative is a special case of left interior multiplication when the multiplier is a vector (i.e. in grade 1).
5.1 Geometric Origins
5.1.1 Outer Multiplication
Outer multiplication is an operation which calculates the value produced by an abstract process Grassmann called evolution, when applied in a geometric context. For the evolution of two vectors 
in Figure 5.1, the vector 
is translated in the direction of the vector 
.
Figure 5.1 Outer multiplication of unequal vectors.
Grassmann interpreted the process of evolution as generating the area swept over by vector during the act of the process. The result of the evolution is the ...
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