ABSTRACT
Now that we have introduced vector spaces, we can move on to the next main object in linear algebra: linear transformations. These are functions between vector spaces that behave nicely with respect to the two fundamental operations on a vector space: addition and scalar multiplication. Differentiation and taking integrals are two important examples of linear transformation. Regarding the nice behavior, note for example that if we take the derivative of the sum of two functions, it is the same as if we would take the derivative of each and then the sum. Let us start with the precise definition.
