K-frame
In linear algebra, a k-frame is an ordered set of k'' linearly independent vectors in a vector space; thus, k ≤ n, where n is the dimension of the space, and an n''-frame is precisely an ordered basis.
If the vectors are orthogonal, or orthonormal, the frame is called an orthogonal frame, or orthonormal frame, respectively.
Properties
- The set of k-frames in a given vector space X is known as the Stiefel manifold, and denoted Vk.
- A k-frame defines a parallelotope ; the volume can be computed via the Gram determinant.
Riemannian geometry
- Orthonormal frame
- Moving frame