变对角最小算子范数埃尔米特矩阵的一个刻划
A characterization of Hermitian matrices with variable diagonal and smallest operator norm
摘要：
本文描述了M_n（C）中的Hermitian方阵M的性质等价于具有最小商范数的性质：||M|| <= ||M+D||对于M_n（C）中的所有实对角矩阵D，||||运营商规范这些矩阵与某些特殊的正矩阵有关，它们的值域包含在特征值的特征空间中。||M||及─| |M||分枝我们展示了如何建设性的方法可以用来获得最小的矩阵的任何维度有关这个问题的优势结果在R^n。
英文摘要：
We describe properties of a Hermitian square matrix M in M_n(C) equivalent to that of having minimal quotient norm in the following sense: ||M|| <= ||M+D|| for all real diagonal matrices D in M_n(C) and || || the operator norm. These matrices are related to some particular positive matrices with their range included in the eigenspaces of the eigenvalues +||M|| and -||M|| of M. We show how a constructive method can be used to obtain minimal matrices of any dimension relating this problem with majorization results in R^n.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
