  Given an automorphism and an anti-automorphism of a semigroup of a Geometric
Algebra, then for each element of the semigroup a (generalized) projection
operator exists that is defined on the entire Geometric Algebra. A single
fundamental theorem holds for all (generalized) projection operators. This
theorem makes previous projection operator formulas equivalent to each other.
The class of generalized projection operators includes the familiar subspace
projection operation by implementing the automorphism `grade involution' and
the anti-automorphism `inverse' on the semigroup of invertible versors. This
class of projection operators is studied in some detail as the natural
generalization of the subspace projection operators. Other generalized
projection operators include projections onto any invertible element, or a
weighted projection onto any element. This last projection operator even
implies a possible projection operator for the zero element.
