Definition:Balanced Set/Also defined as
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Balanced Set: Also defined as
A subset $A$ of a vector space $V$ over a field $\GF \in \set {\R, \C}$ is also by some sources defined as a balanced set if and only if:
- $\forall x \in A: \forall s \in \GF: \cmod s < 1 \implies s x \in A$
Sources
- 2014: Christopher Clapham and James Nicholson: The Concise Oxford Dictionary of Mathematics (5th ed.) ... (previous) ... (next): balanced (of a set)
- 2021: Richard Earl and James Nicholson: The Concise Oxford Dictionary of Mathematics (6th ed.) ... (previous) ... (next): balanced (of a set)