Dimension
The dimension of a vector space ends up being very easy to define once you know what a basis is. One thing we didn't talk about in our previous section is that the basis is the minimum set of vectors needed to span a space, and that the number of vectors in a basis for a particular vector space is always the same.
From this, we define the dimension of a vector space to be equal to the number of vectors it takes as a basis to describe a vector space. Equivalently, we could say that it is the number of coordinates it takes to describe a vector in the vector space. It follows that the dimension of ℝ2 is two, ℝ3 is three, and ℝn is n.
