In linear algebra, orthogonalization means the following: we start with vectors v₁,...,v_k in an inner product space, most commonly the Euclidean space Rⁿ which are linearly independent and we want to find mutually orthogonal vectors u₁,...,u_k which generate the same subspace as the vectors v₁,...,v_k.

One method for performing orthogonalization is the Gram-Schmidt process.

When performing orthogonalization on a computer, the Householder transformation is usually preferred over the Gram-Schmidt process since it is more numerically stable, i.e. rounding errors tend to have less serious effects.