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.
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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
[edit]- 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.
See also
[edit]Riemannian geometry
[edit]References
[edit]- ^ Tu, Loring W.; Arabia, Alberto (2020). Introductory lectures on equivariant cohomology: with appendices by Loring W. Tu and Alberto Arabia. Annals of mathematics studies. Princeton: Princeton University Press. p. 61. ISBN 978-0-691-19748-7.
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