In mathematics, particularly linear algebra an numerical analysis, the Gram–Schmidt process is a method for orthogonalizing 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, …, vn} and generates an orthogonal set S' = {u1, …, un} that spans the same subspace as S.