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Derivatives of eigenvalues and Jordan frames

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


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