The [[Orthogonal]] [[Set Complement|Complement]] [[Linear Subspace]] of some [[Linear Subspace]] $U$ is a [[Linear Subspace]], $U^\perp$ such that all [[Vector|Vectors]] in $U^\perp$ are [[Orthogonal]] to all [[Vector|Vectors]] in $U$. $\huge \begin{align} U &= \op{Col{(A)}} \\ U^\perp &= \op{Nul}\left( A^\intercal \right) \end{align} $ $\huge \forall U \subseteq \R^n: \dim U + \dim U^\perp = n \\ $