Convexity of some spectral functions on Hermitian matrices
نویسنده
چکیده
We prove in this note the convexity of the functions u ◦ λ and more generally u ◦ λB on the space of Hermitian matrices, for B a fixed positive definite hermitian matrix, when u : R → R ∪ {+∞} is a symmetric convex function which is lower semi-continuous on R, and finite in at least one point of R. This is performed by using some optimisation techniques and a generalized Ky Fan inequality. To cite this article: A. Name1, A. Name2, C. R. Acad. Sci. Paris, Ser. I 340 (2005).
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