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Eigenvalue inequalities for convex and log-convex functions

โœ Scribed by Jaspal Singh Aujla; Jean-Christophe Bourin


Publisher
Elsevier Science
Year
2007
Tongue
English
Weight
148 KB
Volume
424
Category
Article
ISSN
0024-3795

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Let f be a convex function defined on an interval I , 0 ฮฑ 1 and A, B n ร— n complex Hermitian matrices with spectrum in I. We prove that the eigenvalues of f (ฮฑA + (1ฮฑ)B) are weakly majorized by the eigenvalues of ฮฑf (A) + (1ฮฑ)f (B). Further if f is log convex we prove that the eigenvalues of f (ฮฑA +