Structure of a Linear Operator

Garret Sobczyk
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Garret Sobczyk: Universidad de Las Américas, Departamento de Física y Matemáticas

Chapter Chapter 8 in New Foundations in Mathematics, 2013, pp 117-136 from Springer

Abstract: Abstract We show how the basic structure of a linear operator follows from its minimal polynomial. The spectral decomposition of a linear operator follows immediately from the spectral basis of idempotents and nilpotents which was developed in Chap. 1 for modular polynomials. The Jordan form of a linear operator, while technically more difficult, is just a refinement of its more fundamental spectral decomposition.

Keywords: Spectral Basis; Minimal Polynomial; Jordan Normal Form; Spectral Decomposition; Jordan Basis (search for similar items in EconPapers)
Date: 2013
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DOI: 10.1007/978-0-8176-8385-6_8

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