论文标题
强壮的小木 - pólya重排不平等及其应用的矩阵概括
A Matrix Generalization of the Hardy-Littlewood-Pólya Rearrangement Inequality and Its Applications
论文作者
论文摘要
我们证明了对正确定矩阵的耐铁木 - 岩石重排的概括。从iusem和Seeger的意义上讲，不平等可以看作是换倒原则。证明中的重要仪器是特定光谱函数的一阶扰动公式，这可能具有独立的利益。然后将不等式扩展到矩形矩阵。使用我们的主要结果，我们为各种信号处理或机器学习应用程序中遇到的几种类似距离的功能提供了新的不平等现象。
We prove a generalization of the Hardy-Littlewood-Pólya rearrangement inequality to positive definite matrices. The inequality can be seen as a commutation principle in the sense of Iusem and Seeger. An important instrument in the proof is a first-order perturbation formula for a certain spectral function, which could be of independent interests. 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.
