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arXiv · 2006.08144

A Matrix Generalization of the Hardy-Littlewood-P\'olya Rearrangement Inequality and Its Applications

Man-Chung Yue
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Abstract

By analyzing an optimization problem over orthogonal matrices, we prove a generalization of the Hardy-Littlewood-P\'olya 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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Man-Chung Yue. 2020-06-15. A Matrix Generalization of the Hardy-Littlewood-P\'olya Rearrangement Inequality and Its Applications. https://arxiv.org/abs/2006.08144

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