Two vectors are orthogonal if the angle between them satisfies (ie, is perpendicular). Equivalently, this means are orthogonal if and only if . If and are also unit, they're called orthonormal.
Furthermore, a basis is orthonormal if for and . It's possible to construct an orthonormal basis from any basis using the Gram-Schmidt process.
The orthogonal complement of subspace contains all vectors in that are orthogonal to every vector in . The intersection of and is the vector, and the bases of each combined form a basis for .