Quotient space (linear algebra)
We will construct an explicit basis for V/W. Let (w1, . . . , wn) be a basis of W, and extend it to a basis (w1, . . . , wn, v1, . . . , vk) of V. Note that with this notation, dim W = n and dim V = n + k. We claim that (v1 + W, . . . , vk + W) forms a basis of V /W, in other words, ([v1], [v2], . . . , [vk]).