The Expected Norm of a Sum of Independent Random Matrices: An Elementary Approach
The Expected Norm of a Sum of Independent Random Matrices: An Elementary Approach
复制标题
独立随机矩阵之和的期望范数：一种基本方法
DOI：
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发表时间：
2015
期刊：
影响因子：
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通讯作者：
J. Tropp
中科院分区：
文献类型：
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作者：
J. Tropp
在当代应用数学和计算数学中，一个常见的挑战是约束独立随机矩阵之和的谱范数的期望。这个量由随机矩阵的期望平方的范数和由其中一个被加数实现的最大平方范数的期望控制;对随机矩阵的维数也有弱依赖性。本文的目的是给出这个重要不等式的一个完整的初等证明。
In contemporary applied and computational mathematics, a frequent challenge is to bound the expectation of the spectral norm of a sum of independent random matrices. This quantity is controlled by the norm of the expected square of the random matrix and the expectation of the maximum squared norm achieved by one of the summands; there is also a weak dependence on the dimension of the random matrix. The purpose of this paper is to give a complete, elementary proof of this important inequality.