 Gram–Schmidt process

In mathematics, particularly linear algebra and numerical analysis, the Gram–Schmidt process is a method for orthonormalizing a set of vectors in an inner product space, most commonly the Euclidean space R"n" equipped with the standard inner product.The Gram–Schmidt process takes a finite, linearly independent set "S" = {"v"1, ..., "v""k"} for and generates an orthogonal set that spans the same "k"-dimensional subspace of R"n" as "S".