A calculus of the absurd

20.8.5 Orthogonal complement
  • Definition 20.8.2 Let \(\textsf {V}\) be an inner product space, and \(E\) be a subspace of \(\textsf {V}\). We define the orthogonal complement of \(E\) as the set

    \begin{equation} E^{\bot } = \{x \in \textsf {V} : \forall v \in E \big ( x \bot e \big ) \} \end{equation}