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The Structure Theory of Linear Mappings

  • James B. CarrellEmail author
Chapter

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.

Copyright information

© Springer Science+Business Media LLC 2017

Authors and Affiliations

  1. 1.Department of MathematicsUniversity of British ColumbiaVancouverCanada

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