Rahul Sharma (Editor)

K frame

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In linear algebra, a branch of mathematics, a k-frame is an ordered set of k linearly independent vectors in a space; thus k ≤ n, where n is the dimension of the vector space, and if k = n 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 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.

    • References

    K-frame Wikipedia
    (Text) CC BY-SA