标题： 概率分布、列随机矩阵及其线性保持器的控射关系 显示英文标题

标题： Majorizations for probability distributions, column stochastic matrices and their linear preservers

摘要： 本文研究了概率分布和列随机矩阵的控制关系。我们证明了一般的控制关系可以归结为上述提到的集合。我们刻画了保持概率分布控制关系的线性算子，并证明它们与保持向量控制关系的算子是等价的。我们的主要结果完整地刻画了保持列随机矩阵强控制关系的线性算子，揭示出比标准情形更丰富的结构。作为这一刻画的前提，我们解决了刻画零和向量控制关系的线性算子的问题，这为 Ando 和 Li、Poon 的经典结果提供了新的结构洞见。 显示英文摘要

摘要： In this paper, we study majorization for probability distributions and column stochastic matrices. We show that majorizations in general can be reduced to the aforementioned sets. We characterize linear operators that preserve majorization for probability distributions, and show their equivalence to operators preserving vector majorization. Our main result provides a complete characterization of linear preservers of strong majorization for column stochastic matrices, revealing a richer structure of preservers than in the standard setting. As a prerequisite to this characterization, we solve the problem of characterizing linear preservers of majorization for zero-sum vectors, which yields a new structural insight into the classical results of Ando and of Li and Poon.