Derivatives of eigenvalues and Jordan frames

Manuel  V. C.  Vieira

doi:10.3934/naco.2016003

Article Contents

2016, Volume 6, Issue 2: 115-126. Doi: 10.3934/naco.2016003

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Derivatives of eigenvalues and Jordan frames

Manuel V. C. Vieira^1,

1.
Departamento de Matemática, Faculdade de Ciências e Tecnologia & CMA, Universidade Nova de Lisboa, 2829-516 Caparica

Received: December 31, 2014

Revised: April 30, 2016

Published: May 2016

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Abstract

Every element in a Euclidean Jordan algebra has a spectral decomposition. This spectral decomposition is generalization of the spectral decompositions of a matrix. In the context of Euclidean Jordan algebras, this is written using eigenvalues and the so-called Jordan frame. In this paper we deduce the derivative of eigenvalues in the context of Euclidean Jordan algebras. We also deduce the derivative of the elements of a Jordan frame associated to the spectral decomposition.

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Mathematics Subject Classification: Primary: 90C25, 17C27; Secondary: 58B10.

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