The Structure Theory of Linear Mappings

James B. Carrell ()
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James B. Carrell: University of British Columbia, Department of Mathematics

Chapter Chapter 10 in Groups, Matrices, and Vector Spaces, 2017, pp 319-335 from Springer

Abstract: 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.

Keywords: Arbitrary Linear Function; Jordan Chevalley Decomposition; Nilpotent Jordan Block; Jordan Canonical Form; Basic String (search for similar items in EconPapers)
Date: 2017
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DOI: 10.1007/978-0-387-79428-0_10

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