The special manifolds of interest in this book are the Stiefel manifold and the Grassmann manifold. Formally, the Stiefel manifold Vk, m is the space of k frames in the m-dimensional real Euclidean space Rm, represented by the set of m x k matrices X such that X' X = I, where Ik is the k x k identity matrix, k and the Grassmann manifold Gk, m-k is the space of k-planes (k-dimensional hyperplanes) in Rm. We see that the manifold Pk, m-k of m x m orthogonal projection matrices idempotent of rank k corresponds uniquely to Gk, m-k. This book is concerned with statistical analysis on the manifolds...
The special manifolds of interest in this book are the Stiefel manifold and the Grassmann manifold. Formally, the Stiefel manifold Vk, m is the space ...
