Groups, Matrices, and Vector Spaces pp 319-335 | Cite as

# The Structure Theory of Linear Mappings

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## 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.

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