Principal bundle structure of matrix manifolds by Marie Billaud-Friess, Antonio Falco, Anthony Nouy

Abstract

In this paper, we introduce a new geometric description of the manifolds of matrices of fixed rank. The starting point is a geometric description of the Grassmann manifold $\mathbb{G}_r(\mathbb{R}^k)$ of linear subspaces of dimension $r You can download the paper from https://arxiv.org/pdf/1705.04093