Geometric Algebra for Computer Science

C SUBSPACE PRODUCTS RETRIEVED

C.1 OUTER PRODUCT FROM GEOMETRIC PRODUCT

We prove that the outer product defined by (6.10) and (6.11) is consistent with the familiar outer product we had before. We repeat the statements for convenience:

where is the grade involution of B introduced in Section 2.9.5. (Writing the equations in this form makes it easier to lift them to general multivectors B.)

We check the earlier defining properties of Section 2.10.

• If B is a scalar β we get a β = βa = β a.
• If B is a vector, we obtain antisymmetry, as we saw above. ...