An orthogonal set is a subset 
of a vector space 
, with the inner product 
such that 
when 
. That is, the vectors
are mutually perpendicular.
Note that there is no restriction on the lengths of the vectors. If the vectors in an orthogonal set all have length one, then they are an orthonormal set.
More generally, on a vector space over any field equipped with a symmetric bilinear form 
, vectors 
and 
are orthogonal when 
. The usual orthogonal
sets and groups in Euclidean
space can be generalized, with applications to special relativity, differential
geometry, and abstract algebra.
