\begin{definition}[Definition:Orthogonal (Bilinear Form)/Orthogonal Complement]
Let $\mathbb K$ be a field.
Let $V$ be a vector space over $\mathbb K$.
Let $b : V\times V \to \mathbb K$ be a reflexive bilinear form on $V$.
Let $S\subset V$ be a subset.
The '''orthogonal complement of $S$ (with respect to $b$)''' is the set of all $v \in V$ which are orthogonal to all $s \in S$.
This is denoted: $S^\perp$.
If $S = \left\{ {v}\right\}$ is a singleton, we also write $v^\perp$.
Category:Definitions/Bilinear Forms
\end{definition}