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	Categories: Linear algebra Balanced set In linear algebra and related areas of mathematics a balanced set, circled set or disk in a vector space is a set S so that for all scalars α with \|α\| ≤ 1 $\alpha S \subset S$ with $\alpha S := \{\alpha x \mid x \in S\}$ The balanced hull for a set S is the intersection of all balanced sets containing S. Examples in a normed vector space the unit ball is a balanced set Properties the union and intersection of balanced sets is a balanced set a set is absolutely convex if and only if it is convex and balanced Categories: Linear algebra

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