The orthogonal complement of a subspace 
of the vector space 
is the set of vectors which are orthogonal to all elements
of 
.
For example, the orthogonal complement of the space generated by two non proportional
vectors 
,
of the real space 
is the subspace formed by all normal vectors to the plane spanned by 
and 
.
In general, any subspace 
of an inner product space 
has an orthogonal complement 
and
 |
This property extends to any subspace 
of a space 
equipped with a symmetric or differential 
-form or a Hermitian form which is nonsingular on 
.
