chapter  4
88 Pages

& The Structure of Vector Spaces

We have sown our wild oaks (see Section 2.5) and grown subspaces from all manner of sets. Now we will investigate the question as to whether we can reverse-engineer the process. Given a vector space, can we find a small and simple spanning set for the space? Along the way we will also address a more fundamental question: Why do we want to? Why do we care?