Applied Mathematical Methods

15

Vector Spaces: Fundamental Concepts

Chapters till this stage have been devoted to applied linear algebra, in which we have carefully avoided ideas and notions which are too abstract. Abstractions and generalizations are, however, important; even for engineering applications. Therefore, in the present chapter, we briefly summarize some of the relevant and fundamental ideas that are basic for a thorough understanding of linear algebra. After a brief discussion on groups and fields, we define and discuss concepts of vector spaces and linear transformations. Finally, we also make a quick tour of the concept of function spaces, which turn out to be significant later in our study of differential equations and eigenfunction expansion.¹

Group

A set ...