Halfspace

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Consider the hyperplane, LaTeX: \{x \in \mathbb{R}^n: a^T x = b\} (where LaTeX: a \in \mathbb{R}^n \backslash {0}). This partitions LaTeX: \mathbb{R}^n into two (closed) half spaces: LaTeX: \{ x: a^Tx \le b\} and LaTeX: \{ x: a^Tx \ge b\}. The two associated open halfspaces are LaTeX: \{ x: a^t x < b\} and LaTeX: \{ x: a^Tx > b\}.


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