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.