# Orthogonalization

In

linear algebra,

**orthogonalization** means the following: we start with vectors

*v*_{1},...,

*v*_{k} in an

inner product space, most commonly the

Euclidean space **R**^{n} which are

linearly independent and we want to find mutually

orthogonal vectors

*u*_{1},...,

*u*_{k} which generate the same

subspace as the vectors

*v*_{1},...,

*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.