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Comonotonic convex upper bound and majorization

โœ Scribed by Ka Chun Cheung


Book ID
108153174
Publisher
Elsevier Science
Year
2010
Tongue
English
Weight
307 KB
Volume
47
Category
Article
ISSN
0167-6687

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Weak majorization inequalities and conve
โœ Jaspal Singh Aujla; Fernando C. Silva ๐Ÿ“‚ Article ๐Ÿ“… 2003 ๐Ÿ› Elsevier Science ๐ŸŒ English โš– 143 KB

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 +