Hermitian operators and convex functions
Jean-Christophe Bourin
TL;DR
This paper explores inequalities related to eigenvalues of Hermitian operators, extending basic convexity principles to matrix versions involving convex combinations and compressions.
Contribution
It introduces matrix inequalities for eigenvalues of Hermitian operators based on convex functions, generalizing classical convexity inequalities to the matrix setting.
Findings
Derived new eigenvalue inequalities for Hermitian operators.
Extended convexity inequalities to matrix and operator contexts.
Provided theoretical foundations for matrix convex functions.
Abstract
Several inequalities for eigenvalues involving convex combinations and compressions are given. These inequalities are matrix version of the basic convexity inequality f((a+b)/2) < (f(a)+f(b))/2.
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Taxonomy
TopicsMathematical Inequalities and Applications · Matrix Theory and Algorithms · Analytic and geometric function theory