The Structure Theory of Linear Mappings

Abstract

Throughout this chapter, V will be a finite-dimensional vector space over $${\mathbb F}$$. Our goal is to prove two theorems that describe the structure of an arbitrary linear mapping $$T:V\rightarrow V$$having the property that all the roots of its characteristic polynomial lie in $${\mathbb F}$$. To describe this situation, let us say that $${\mathbb F}$$contains the eigenvalues of T. Recall that a linear mapping $$T:V\rightarrow V$$is also called an endomorphism of V, and in this chapter, we will usually use that term.