| On the Reduced Minimum Modulus of Projections and the Angle between Two Subspaces |
| Received:December 20, 2008 Revised:June 30, 2009 |
| Key Words:
subspace angle between two subspaces reduced minimum modulus.
|
| Fund Project:Supported by the National Natural Science Foundation of China (Grant No.10871224) and the Fundamental Research Funds for the Central Universities (Grant No.GK 200902049). |
|
| Hits: 2947 |
| Download times: 2294 |
| Abstract: |
| Let $\mathcal{M}$ and ${\mathcal{N}}$ be nonzero subspaces of a Hilbert space $\mathcal{H},$ and $P_{\mathcal{M}}$ and $P_{\mathcal{N}}$ denote the orthogonal projections on $\mathcal{M}$ and ${\mathcal{N}},$ respectively. In this note, an exact representation of the angle and the minimum gap of $\mathcal{M}$ and ${\mathcal{N}}$ is obtained. In addition, we study relations between the angle, the minimum gap of two subspaces $\mathcal{M}$ and ${\mathcal{N}},$ and the reduced minimum modulus of $(I-P_{\mathcal{N}})P_{\mathcal{M}}$. |
| Citation: |
| DOI:10.3770/j.issn:1000-341X.2011.01.019 |
| View Full Text View/Add Comment |
