Geometric products

The geometric product is the fundamental product of geometric algebra. There are two products with symmetric properties called the geometric product and geometric antiproduct.

Geometric Product
The following Cayley table shows the geometric products between all pairs of basis elements in the 5D conformal geometric algebra $$\mathcal G_{4,1}$$. The identity of the geometric product is the scalar basis element $$\mathbf 1$$.

Cells colored yellow correspond to the contribution from the wedge product, and cells colored orange correspond to the contribution from the dot product.



Geometric Antiproduct
The following Cayley table shows the geometric antiproducts between all pairs of basis elements in the 5D conformal geometric algebra $$\mathcal G_{4,1}$$. The identity of the geometric antiproduct is the antiscalar basis element $${\large\unicode{x1D7D9}}$$.

Cells colored yellow correspond to the contribution from the antiwedge product, and cells colored orange correspond to the contribution from the antidot product.