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 \(V\).

Proofs: 1

Definitions: 1
Examples: 2
Proofs: 3
Propositions: 4

Thank you to the contributors under CC BY-SA 4.0!



Adapted from CC BY-SA 3.0 Sources:

  1. Brenner, Prof. Dr. rer. nat., Holger: Various courses at the University of Osnabrück