CHAPTER 2 - Vector Spaces

Abstract

This chapter describes vector spaces. The concept of a vector space is fundamental for a linear associative algebra. A vector space is a special case of a general algebraic discipline, called a module over a ring. The notion of a vector space can be generalized in various ways. Every vector space with more than one element has a basis. Isomorphism is an equivalence relation in any set of vector spaces over the same field. However, two isomorphic vector spaces are algebraically indistinguishable. If a vector space is not finite dimensional then it is called an infinite dimensional vector space.