K-frame
From Wikipedia, the free encyclopedia
In linear algebra, a k-frame is an ordered set of k linearly independent vectors in a vector space[1]; 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 (particularly the set of orthonormal k-frames) in a given vector space X is known as the Stiefel manifold, and denoted Vk(X).
- A k-frame defines a parallelotope (a generalized parallelepiped); the volume can be computed via the Gram determinant.
