Spaces of linear maps
11.1 A look at (U, V)
In the first part of this book we looked at n-dimensional vector spaces as generalisations of two and three dimensional spaces. In this part we look at n-dimensional vector spaces with an eye to generalisation to infinite dimensional spaces.
We looked mainly at linear maps of a vector space into itself (the so-called endomor-phisms). For various reasons, some of which we consider in the next section, these are often the most interesting, but it is worth looking at the more general case.
Let us start with the case when U and V are finite dimensional. We begin by generalising Definition 6.1.1.