主子矩阵特征值的边界不等式

线性代数与矩阵理论研究进展(英文) Pub Date : 2019-06-30 DOI:10.4236/ALAMT.2019.92002

A. Dax

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引用次数: 2

摘要

Ky Fan迹定理和柯西和庞加莱的交错定理是表征厄米矩阵的重要观察结果。在这篇笔记中，我们引入一类新的不等式来扩展这些定理。新的不等式是通过用它们的模替换特征值和对角线项而得到的。这种修正产生了有效的边界不等式，它在更大范围的矩阵上有效。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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Bounding Inequalities for Eigenvalues of Principal Submatrices

Ky Fan trace theorems and the interlacing theorems of Cauchy and Poincare are important observations that characterize Hermitian matrices. In this note, we introduce a new type of inequalities which extend these theorems. The new inequalities are obtained from the old ones by replacing eigenvalues and diagonal entries with their moduli. This modification yields effective bounding inequalities which are valid on a larger range of matrices.

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线性代数与矩阵理论研究进展(英文)

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