Geometric invariants using geometry algebra

In this paper, we interpret the fundamental geometric invariants in a new framework: geometric algebra (GA). The study of such geometric invariance is a field of active research. The homogeneous model (Grassmann model) is selected for different kinds of geometric invariants, including Euclidean invariants, Projective invariants etc. GA focuses on the subspace of a vector space as elements of computation. Linear transformation can be extended to the subspace structure. The paper compares the meaning of invariants using the new model with that using the traditional one. This work shows that geometric algebra is a very elegant language for expressing geometric objects.