In studying vector spaces, I came across the coset of a vector space.(adsbygoogle = window.adsbygoogle || []).push({});

We have an equivalence relation defined as

u = v [itex]\rightarrow[/itex] u-v [itex]\in[/itex] W

where W is a subspace of V.

the equivalence class that u belongs to is u + W. I can see why u must belong to this equivalence class ( the coset) because of reflexivity, but why W?

Is u - W [itex]\in[/itex] W ?

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# Cosets and Vector Spaces Question

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