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.