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 bivector can be calculated by multiplying the matrices:
So the complete geometric multiplication table is:
a*b |
b.e |
b.e1 |
b.e2 |
b.e12 |
| a.e |
|
|
|
|
| a.e1 |
|
|
|
|
| a.e2 |
|
|
|
|
| a.e12 |
|
|
|
|
which is equivilant to the table derived here.
Any multivector can be represented by a single matrix representing a linear sum of these basis, for instance,
Further Reading
Other uses of Pauli Matrix:
Related Concepts:
