# Orthogonal complement

Orthogonal complement of a subspace, $LaTeX: S.$ $LaTeX: \textstyle \left \{y: yx = 0 \mbox{ for all } x \in S \right \}.$ In particular, if $LaTeX: \textstyle S = \left \{x: x = Av \mbox{ for some } v \in \mathbb{R}^n \right \},$ where $LaTeX: A$ is an $LaTeX: \textstyle m \times n$ matrix, its orthogonal complement is $LaTeX: \textstyle \left \{y: yA = 0 \right \}.$