Stiefel manifold

In mathematics, the Stiefel manifold V_k(R) is the set of all orthonormal k-frames in R. That is, it is the set of ordered k-tuples of orthonormal vectors in R. It is named after Swiss mathematician Eduard Stiefel. Likewise one can define the complex Stiefel manifold V_k(C) of orthonormal k-frames in C and the quaternionic Stiefel manifold V_k(H) of orthonormal k-frames in H. More generally, the construction applies to any real, complex, or quaternionic inner product space.