The Projective Group as a Topological Manifold

• 作者: Jean-Francois Niglio
• 来源期刊: 线性代数与矩阵理论研究进展(英文)
• 学科: 数学
• 关键词: Projection ORTHOGONAL Projections PROJECTIVE OPERATORS PROJECTIVE MANIFOLDS
• 年，卷（期）: 2018,（4）
• 页码范围: 134-142
• 页数: 9页
• 分类号: O1

摘要

In this article, we start by a review of the circle group? [1] and its topology induced [1] by the quotient metric, which we later use to define a topological structure on the unit circle . Using points on? under the complex exponential map, we can construct orthogonal projection operators. We will show that under this construction, we arrive at a topological group, denoted? of projection matrices. Together with the induced topology, it will be demonstrated that? is Hausdorff and Second Countable forming a topological manifold. Moreover, I will use an example of a group action on? to generate subgroups of?.