The orthogonal complement of a subspace of the vector space is the set of vectors which are orthogonal to all elements of . For example, the orthogonal complement of the space generated by two non proportional vectors , of the real space is the subspace formed by all normal vectors to the plane spanned by and .
In general, any subspace of an inner product space has an orthogonal complement and
This property extends to any subspace of a space equipped with a symmetric or differential -form or a Hermitian form which is nonsingular on .