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Rudolph, G. and Schmidt, M. (2103) Differential Geometry and Mathematical Physics: Part I Manifold, Lie Groups and Hamiltonian Systems. ISBN 978-94-007-5344-0, Springer, Berlin.

has been cited by the following article:

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

    AUTHORS: Jean-Francois Niglio

    KEYWORDS: Projection Theory, Projection Manifolds, Projectors, Congruent Projection Matrices

    JOURNAL NAME: Advances in Linear Algebra & Matrix Theory, Vol.9 No.1, March 29, 2019

    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.