The name 'Geometric algebra
' is preferred when the geometric
properties of the system are emphasized. This is usually desired in physics
and other application
s, because this algebra helps people visualize
the problem and understand it in a more tangible
On the other hand, an algebra as such is completely abstract. All possible calculations of Clifford algebra can be done on an abstract level, for example in a matrix representation. If this is sufficient, it is quite pointless to use geometric algebra in the first place.