Bounding Inequalities for Eigenvalues of Principal Submatrices

• 作者: Achiya Dax
• 来源期刊: 线性代数与矩阵理论研究进展(英文)
• 学科: 数学
• 关键词: Cauchy INTERLACING THEOREM POINCARÉ INTERLACING THEOREM Ky Fan Trace Theorems NON-HERMITIAN MATRICES Normal MATRICES Bounding INEQUALITIES
• 年，卷（期）: 2019,（2）
• 页码范围: 21-34
• 页数: 14页
• 分类号: O1

摘要

Ky Fan trace theorems and the interlacing theorems of Cauchy and Poincaré 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.