An orthogonal complement to a subspace is the vector perpendicular to all the vectors in that subspace. A common example is a plane's normal vector. A normal is the orthogonal complement of a plane. The following are formulas that relate kernels and images. You should know these formulas. In the following the orthogonal complement of 
will be denoted as 
(pronounced: S-perp). 
will be denoted as (pronounced: S-perp).