Derivatives of eigenvalues and Jordan frames

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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 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 languageEnglish
Pages (from-to)114-125
JournalNumerical Algebra, Control and Optimization
Volume6
Issue number2
DOIs
Publication statusPublished - 1 Jun 2016

Keywords

  • Differentiability
  • Eigenvalues
  • Euclidean Jordan algebras
  • Symmetric cones

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