Orthogonal

In elementary geometry, orthogonal is the same as perpendicular. Two lines or curves are orthogonal if they are perpendicular at their point of intersection. Two vectors  and  of the real plane  or the real space  are orthogonal iff their dot product . This condition has been exploited to define orthogonality in the more abstract context of the -dimensional real space .

More generally, two elements  and  of an inner product space  are called orthogonal if the inner product of  and  is 0. Two subspaces  and  of  are called orthogonal if every element of  is orthogonal to every element of . The same definitions can be applied to any symmetric or differential k-form and to any Hermitian form.