Summary

We have covered a bit of ground around describing vector spaces in this chapter. We've seen how a vector space has subspaces and how to test whether a set of vectors is a subspace. We've rigorously defined linear combinations and derived the concept of linear independence from it. We've also learned multiple ways to describe a vector space through the span and basis. From this, we've learned the true meaning of coordinates and put all that together to define the dimension of a vector space. In the next chapter, we will look at how to transform vectors in these vector spaces using matrices!