Gram-Schmidt Algorithm
A Gram-Schmidt Algorithm is a vector orthonomralising algorithm that ...
- AKA: Gram–Schmidt Process.
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- Counter-Example(s):
- See: QR Decomposition Algorithm, Triangular Matrix, Orthonormal Basis, Inner Product Space, Euclidean Space, Linearly Independent, Orthogonal Set.
References
2015
- (Wikipedia, 2015) ⇒ http://en.wikipedia.org/wiki/Gram–Schmidt_process Retrieved:2015-12-27.
- In mathematics, particularly linear algebra and numerical analysis, the Gram–Schmidt process is a method for orthonormalising a set of vectors in an inner product space, most commonly the Euclidean space Rn. The Gram–Schmidt process takes a finite, linearly independent set S = {v1, ..., vk} for and generates an orthogonal set that spans the same k-dimensional subspace of Rn as S.
The method is named after Jørgen Pedersen Gram and Erhard Schmidt but it appeared earlier in the work of Laplace and Cauchy. In the theory of Lie group decompositions it is generalized by the Iwasawa decomposition.
The application of the Gram–Schmidt process to the column vectors of a full column rank matrix yields the QR decomposition (it is decomposed into an orthogonal and a triangular matrix).
- In mathematics, particularly linear algebra and numerical analysis, the Gram–Schmidt process is a method for orthonormalising a set of vectors in an inner product space, most commonly the Euclidean space Rn. The Gram–Schmidt process takes a finite, linearly independent set S = {v1, ..., vk} for and generates an orthogonal set that spans the same k-dimensional subspace of Rn as S.