Vector subspace

A vector subspace is a vector space that is a subset of another vector space. This means that all the properties of a vector space are satisfied.
Let "W" be a non empty subset of a vector space "V", then, "W" is a vector subspace if and only if the next 3 conditions are satisfied:
If formula_1 and formula_2 are subspaces of a vector space formula_3, then the sum and the direct sum of formula_1 and formula_2, denoted respectively by formula_6 and formula_7, are subspaces as well.