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

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.