Orthogonalization
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.