Cosets

Let W be any subspace of a vector space V over the field F.Let α be any element of V then the set { α+λ: λ∊W } is called left coset of W in V generated by α. This set is denoted by α+W.

Thus

          α +W={ α+λ : λ∊W } (Left coset )

Similarly, the set

W+ α ={ α +λ : ∊W } is right coset of W in V generated by α.