: Mathématiques: Gram-Schmidt process

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Gram-Schmidt process

In mathematics, particularly linear algebra and numerical analysis, the Gram–Schmidt process or Gram-Schmidt algorithm is a method for orthonormalizing a set of vectors in an inner product space, most commonly the Euclidean space Rⁿ equipped with the standard inner product. The Gram–Schmidt process takes a finite, linearly independent set of vectors $S = {v 1, ..., v k}$ for $k \leq n$ and generates an orthogonal set $S' = {u 1, ..., u k}$ that spans the same k-dimensional subspace of Rⁿ as S.
(Wikipedia, The Free Encyclopedia, https://en.wikipedia.org/wiki/Gram%E2%80%93Schmidt_process)

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