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Convexity and differentiability properties of spectral functions and spectral mappings on Euclidean Jordan algebras
- Source :
-
Linear Algebra & its Applications . Apr2007, Vol. 422 Issue 2/3, p664-700. 37p. - Publication Year :
- 2007
-
Abstract
- Abstract: We study in this paper several properties of the eigenvalues function of a Euclidean Jordan algebra, extending several known results in the framework of symmetric matrices. In particular, we give a concise form for the directional differential of a single eigenvalue. We especially focus on spectral functions F on Euclidean Jordan algebras, which are the composition of a symmetric real-valued function f with the eigenvalues function. We explore several properties of f that are transferred to F, in particular convexity, strong convexity and differentiability. Spectral mappings are also considered, a special case of which is the gradient mapping of a spectral function. Answering a problem proposed by H. Sendov, we give a formula for the Jacobian of these functions. [Copyright &y& Elsevier]
- Subjects :
- *SYMMETRIC matrices
*UNIVERSAL algebra
*EIGENVALUES
*MATHEMATICS
Subjects
Details
- Language :
- English
- ISSN :
- 00243795
- Volume :
- 422
- Issue :
- 2/3
- Database :
- Academic Search Index
- Journal :
- Linear Algebra & its Applications
- Publication Type :
- Academic Journal
- Accession number :
- 24220427
- Full Text :
- https://doi.org/10.1016/j.laa.2006.11.025