Derivatives of eigenvalues and Jordan frames

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.