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:[1][2]
If and are subspaces of a vector space , then the sum and the direct sum of and , denoted respectively by and ,[3] are subspaces as well.[4]