# American Institute of Mathematical Sciences

2016, 6(2): 115-126. doi: 10.3934/naco.2016003

## Derivatives of eigenvalues and Jordan frames

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

Received  January 2015 Revised  May 2016 Published  June 2016

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.
Citation: Manuel V. C. Vieira. Derivatives of eigenvalues and Jordan frames. Numerical Algebra, Control & Optimization, 2016, 6 (2) : 115-126. doi: 10.3934/naco.2016003
##### References:

show all references

##### References:
 [1] Ying Lin, Qi Ye. Support vector machine classifiers by non-Euclidean margins. Mathematical Foundations of Computing, 2020, 3 (4) : 279-300. doi: 10.3934/mfc.2020018 [2] Lei Liu, Li Wu. Multiplicity of closed characteristics on $P$-symmetric compact convex hypersurfaces in $\mathbb{R}^{2n}$. Discrete & Continuous Dynamical Systems - A, 2020  doi: 10.3934/dcds.2020378

Impact Factor: