Khan Academy: Linear Algebra: The Gram Schmidt Process

Video about the Gram-Schmidt process which is used to create an orthonormal basis from any basis. First an orthonormal basis is created in one dimension by normalizing the vector and then in two dimensions by building on the one-dimensional basis and creating an orthogonal vector. The second vector is solved for by using the properties of projections onto a subspace when the basis is orthonormal and then normalized. A similar process is used to create an orthonormal basis in three and four dimensions. [19:24]