Commutativity and spectra of Hermitian matrices
Commutativity and spectra of Hermitian matrices
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DOI：
10.1016/0024-3795(94)90399-9
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发表时间：
1994-11
影响因子：
1.1
通讯作者：
W. So
中科院分区：
文献类型：
--
作者：
W. So
如果两个厄米特矩阵可交换，则它们的和的特征值就是这两个矩阵的特征值在适当的阶下的和。例子表明，匡威一般不成立。本文得到了部分逆。该技术涉及的平等外尔不等式的情况下的表征。此外，给出了两个具有性质的Hermite矩阵的交换性的一个新的证明，并给出了两个正定Hermite矩阵乘积的类似结果。
If two Hermitian matrices commute, then the eigenvalues of their sum are just the sums of the eigenvalues of the two matrices in a suitable order. Examples show that the converse is not true in general. In this paper, partial converses are obtained. The technique involves a characterization of the equality cases for Weyl's inequalities. Moreover, a new proof on the commutativity of two Hermitian matrices with propertyLand analogous results for the product of two positive definite Hermitian matrices are included.