Derivatives of eigenvalues and Jordan frames

Manuel V C Vieira

doi:10.3934/naco.2016003

Derivatives of eigenvalues and Jordan frames

Manuel V C Vieira

DM - Departamento de Matemática

Research output: Contribution to journal › Article

1 Citation (Scopus)

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 de- duce 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.

Original language	English
Pages (from-to)	114-125
Journal	Numerical Algebra, Control and Optimization
Volume	6
Issue number	2
DOIs	https://doi.org/10.3934/naco.2016003
Publication status	Published - 1 Jun 2016

Keywords

Differentiability
Eigenvalues
Euclidean Jordan algebras
Symmetric cones

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