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An inequality for convex functions involving majorization

✍ Scribed by Albert W Marshall; Frank Proschan


Book ID
107798762
Publisher
Elsevier Science
Year
1965
Tongue
English
Weight
154 KB
Volume
12
Category
Article
ISSN
0022-247X

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