Convexity and differentiability properties of spectral functions and spectral mappings on Euclidean Jordan algebras
作者： Michel Baes
DOI: 10.1016/J.LAA.2006.11.025
关键词: Differential form 、 Algebra 、 Pure mathematics 、 Symmetric matrix 、 Function (mathematics) 、 Mathematics 、 Convexity 、 Eigenvalues and eigenvectors 、 Differentiable function 、 Jordan algebra 、 Symmetric function
摘要: Abstract We study in this paper several properties of the eigenvalues function a Euclidean Jordan algebra, extending known results framework symmetric matrices. In particular, we give concise form for directional differential single eigenvalue. especially focus on spectral functions F algebras, which are composition real-valued f with function. explore that transferred to F, particular convexity, strong convexity and differentiability. Spectral mappings also considered, special case is gradient mapping Answering problem proposed by H. Sendov, formula Jacobian these functions.
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