Orthogonalization

In linear algebra, orthogonalization is the process of finding a set of orthogonal vectors that span a particular subspace. Formally, starting with a linearly independent set of vectors {v₁,...,v_k} in an inner product space (most commonly the Euclidean space Rn), orthogonalization results in a set of orthogonal vectors {u₁,...,u_k} that generate the same subspace as the vectors v₁,...,v_k. Every vector in the new set is orthogonal to every other vector in the new set; and the new set and the old set have the same linear span.