The Gram–Schmidt process is a method for orthonormalising 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 S = {v1, ..., vk} for k ≤ n and generates an orthogonal set S′ = {u1, ..., uk} that spans the same k-dimensional subspace of Rn as S.
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