The basis vectors can be represented by matrices, this algebra was worked out independently by Pauli for his work on quantum mechanics, we can define the following equivalents:
The scalar would be the identity matrix.
The bivectors can be calculated by multiplying the matrices:
The trivector is:
So the complete geometric multiplication table is:
a*b 
b.e 
b.e1 
b.e2 
b.e3 
b.e12 
b.e31 
b.e23 
b.e123 
a.e 








a.e1 








a.e2 








a.e3 








a.e12 








a.e31 








a.e23 








a.e123 








which is equivalent to the table derived here.
Further Reading
Other uses of Pauli Matrix:
Related Concepts:
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