Lie Groups and Lie Algebras

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

Chapter Chapter 18 in New Foundations in Mathematics, 2013, pp 329-351 from Springer

Abstract: Abstract We have studied linear transformation on $${\mathbb{R}}^{n}$$ using the traditional matrix formalism in Chap. 7 and more generally in Chaps. 8–10, using the machinery of geometric algebra. This chapter explains the bivector interpretation of a general linear operator and offers a new proof of the Cayley–Hamilton theorem based upon this interpretation.

Keywords: Geometric Algebra; General Linear Operator; Bivector Representation; Dynkin Diagram; Cartan Matrix (search for similar items in EconPapers)
Date: 2013
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-0-8176-8385-6_18

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DOI: 10.1007/978-0-8176-8385-6_18

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