Stiefel manifold ($V_k({\mathbb{R}}^n)$)

The Stiefel manifold, denoted as \( V_k(\mathbb{R}^n) \), is a mathematical object that describes the space of orthonormal k-frames in an n-dimensional Euclidean space \(\mathbb{R}^n\). More specifically, it consists of all matrices \( A \in \mathbb{R}^{n \times k} \) whose columns are orthonormal vectors in \(\mathbb{R}^n\).