Weak majorization inequalities and conve
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Jaspal Singh Aujla; Fernando C. Silva
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Article
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2003
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Elsevier Science
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English
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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 +