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

作     者：Jean-Francois Niglio 

作者机构：Department of Mathematics Kingston University London UK 

出 版 物：《Advances in Linear Algebra & Matrix Theory》 (线性代数与矩阵理论研究进展（英文）)

年 卷 期：2019年第9卷第1期

页      面：1-19页

学科分类：07[理学] 0701[理学-数学] 070101[理学-基础数学] 

主　　题：Projection Theory Projection Manifolds Projectors Congruent Projection Matrices 

摘      要：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.