where is a quadratic form associated with (in an inner product space, ).
Hence for an orthogonal basis
where and are components of and in the basis.
The concept of orthogonality may be extended to a vector space (over any field) equipped with a quadratic form . Starting from the observation that, when the characteristic of the underlying field is not 2, the associated symmetric bilinear form allows vectors and to be defined as being orthogonal with respect to when