Linear mappings

Abstract

In the study of any algebraic structure there are two concepts that are of paramount importance. The first is that of a substructure (i.e. a subset with the same type of structure), and the second is that of a morphism (i.e. a mapping from one structure to another that is ‘structure-preserving’). So far we have encountered the notion of a substructure for vector spaces; this we called a subspace. In this Chapter we shall consider the notion of a morphism between vector spaces, that is a mapping f from one vector space to another that is ‘structure-preserving’ in the following sense.