On some convexity and monotonicity inequalities of Elliott Lieb
Eric A. Carlen
TL;DR
This paper reviews and provides new proofs for a set of matrix inequalities related to convexity and monotonicity, originally established by Elliott Lieb in 1973, highlighting their significance in mathematical analysis.
Contribution
It offers a comprehensive review of Lieb's inequalities with new proofs, connecting various developments in matrix inequalities since 1973.
Findings
New proofs of classical inequalities
Connections between convexity and monotonicity in matrix analysis
Enhanced understanding of Lieb's foundational results
Abstract
A fundamental paper of Elliott Lieb from 1973 has been the basis for much beautiful work on matrix inequalities by many people over the following years. We review a well-connected set of these developments. Some new proofs are provided.
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Taxonomy
TopicsMathematical Inequalities and Applications · Matrix Theory and Algorithms · Advanced Optimization Algorithms Research