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| Autor principal: | |
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| Formato: | Preprint |
| Publicado: |
2023
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| Materias: | |
| Acceso en línea: | https://arxiv.org/abs/2309.11596 |
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- To any $V$ in the Grassmannian ${\rm Gr}_k({\mathbb R}^n)$ of $k$-dimensional vector subspaces in ${\mathbb R}^n$ one can associate the diagonal entries of the ($n\times n$) matrix corresponding to the orthogonal projection of ${\mathbb R}^n$ to $V$. One obtains a map ${\rm Gr}_k({\mathbb R}^n)\to {\mathbb R}^n$ (the Schur-Horn map). The main result of this paper is a criterion for pre-images of vectors in ${\mathbb R}^n$ to be connected. This will allow us to deduce connectivity criteria for a certain class of subspaces of the real Stiefel manifold which arise naturally in frame theory. We extend in this way results of Cahill, Mixon, and Strawn.