What is the difference between a basis and a group of vectors which span the space? The two properties for a basis is for the vectors to be linearly independent and to span the space. Given a family of vectors, let's say their linear combinations generate the whole space; then they are said to span the space - so then they must be linearly independent. A trivial example is the unit vectors. I've read numerous times they're a spanning set, and on the other hand they're a basis?