Vector Spaces and Linear Maps

Abstract

The linear structure of $\mathbb{K}^n$ is shared by several mathematical objects. We have already noticed that the set of mxn matrices satisfies the laws of sum and multiplication by scalars. The aim of this chapter is to introduce abstract language and illustrate some facts related to linear structure. In particular, we shall see that in every finite-dimensional vector space we can introduce the coordinates related to a basis and explain how the coordinates description of intrinsic objects changes when we change the coordinates, i.e., the basis.