A Follow-Up on Projection Theory: Theorems and Group Action

Abstract

In this article, we wish to expand on some of the results obtained from the first article entitled Projection Theory. We have already established that one-parameter projection operators can be constructed from the unit circle . As discussed in the previous article these operators form a Lie group known as the Projection Group. In the first section, we will show that the concepts from my first article are consistent with existing theory [1] [2]. In the second section, it will be demonstrated that not only such operators are mutually congruent but also we can define a group action on  by using the rotation group [3] [4]. It will be proved that the group acts on elements of  in a non-faithful but ∞-transitive way consistent with both group operations. Finally, in the last section we define the group operation  in terms of matrix operations using the operator and the Hadamard Product; this construction is consistent with the group operation defined in the first article.