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<p>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.</p>

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

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2025年12月24日

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  • Man-Chung Yue

摘要

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.