Vector Spaces

Abstract

In this chapter you will learn

• the operations on the classical vector spaces ${\mathbb{R}}^{2}$, ${\mathbb{R}}^{3}$ and ${\mathbb{R}}^{n}$,

• the vector space as the central algebraic structure of linear algebra,

• the linear map**s as the homomorphisms of vector spaces,

• the concepts of linear independence, basis and dimension of vector spaces, and how they are related,

• the calculation with coordinates with respect to different bases of a vector space.