Can someone explain the difference between a subspace and a vector space? I realize that a vector space has 10 axioms that define how vectors can be added and subtracted. I also realize that a subspace is closed under multiplication, addition, and contains the zero vector. My problem is that I fundamentally don't understand the difference between them.
Perhaps you guys could show me some examples of both a vector space and subspace. I'm a visual learner. Thanks. :)