A Matrix Generalization of the Hardy-Littlewood-Pólya Rearrangement Inequality and Its Applications

2020/06/15 by Yue, Man-Chung
#FOS: Mathematics #Functional Analysis (math.FA)

paper · doi:10.48550/arxiv.2006.08144

Abstract

By analyzing an optimization problem over orthogonal matrices, we prove a generalization of the Hardy-Littlewood-Pólya rearrangement inequality to positive definite matrices. The inequality is then extended to rectangular matrices. Using our main results, we derive new inequalities for several distance-like functions encountered in various signal processing or machine learning applications.

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