- #1
Master J
- 226
- 0
In studying vector spaces, I came across the coset of a vector space.
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 ?
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 ?