Geometric algebra is the Clifford algebra generated by a vector space 
with quadratic form 
, subject to
 |
for every 
.
For an inner product space, the geometric product
of vectors decomposes as
 |
where the symmetric part is the dot product and the antisymmetric part is the wedge product. Scalars, vectors, bivectors, and elements of higher grade therefore belong to a single associative algebra.
