Orthogonal complement

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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 \}.


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