Gram-Schmidt Process

The Gram-Schmidt process is a method for constructing an orthonormal basis from a set of vectors in an inner product space, most commonly Euclidean space with the standard inner product. It takes a finite, linearly independent set of vectors and generates an orthogonal set spanning the same subspace, and it is named after Jorgen Pedersen Gram and Erhard Schmidt, though Pierre-Simon Laplace had been familiar with the method earlier; applying it to the columns of a full column rank matrix yields the QR decomposition.