Elementary vector

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Let LaTeX: V be a subspace of LaTeX: \mathbb{R}^n. For LaTeX: v \in S, let LaTeX: S(v) denote its support set: LaTeX: \{j: v_j \neq 0\}. Then, LaTeX: v is an elementary vector of LaTeX: V if there does not exist LaTeX: v' \in V such that LaTeX: v' \neq 0 and LaTeX: S(v') \subseteq S(v). This extends to where LaTeX: V is not a subspace, such as the collection of non-negative vectors inLaTeX: \mathbb{R}^n, in which case LaTeX: S(v) is the set of coordinates with positive value. This is of particular importance in defining the optimal partition of an LP solution.


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