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Lemma: Equivalency of Vectors in Vector Space If their Difference Forms a Subspace
Let \(V\) be a vector space over a field \(F\) and let \(U\subseteq V\) be its subspace. Then the relation defined by $v\sim w \Longleftrightarrow v-w\in U$ is an equivalence relation on \(V\).
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Adapted from CC BY-SA 3.0 Sources:
- Brenner, Prof. Dr. rer. nat., Holger: Various courses at the University of Osnabrück