On the eigenvalues and diagonal entries of a Hermitian matrix
type: Item
instance of: scholarly article
title: On the eigenvalues and diagonal entries of a Hermitian matrix
zbMATH Open document ID: 0767.15014
DOI: 10.1016/0024-3795(93)90317-H
author: Enzhong Fu
author: Thomas L. Markham
published in: Linear Algebra and its Applications
publication date: 1993-05-16T00:00:00Z
review text: Let \(A=[a_{ij}]\) be an \(n\times n\) Hermitian matrix, and let \(\lambda_ 1\geq\lambda_ 2 \geq\dots\geq \lambda_ n\) be its eigenvalues. Suppose that, for some \(k\), \(\lambda_ 1+\lambda_ 2 +\dots+\lambda_ k=a_{11}+ a_{22}+\dots+ a_{kk}\). Then the authors show that \(A\) is block diagonal of the form \(\text{diag}(A_ 1,A_ 2)\) where the blocks \(A_ 1\), \(A_ 2\) are \(k\times k\) and \((n-k)\times(n- k)\), respectively.
reviewed by: John D. Dixon
Mathematics Subject Classification ID: 15B57
Mathematics Subject Classification ID: 15A42
Mathematics Subject Classification ID: 15A18
zbMATH DE Number: 166243
zbMATH Keywords: Hermitian matrix
zbMATH Keywords: eigenvalues
zbMATH Keywords: block diagonal
MaRDI profile type: Publication
cites work: Doubly Stochastic Matrices and the Diagonal of a Rotation Matrix
cites work: Inequalities: theory of majorization and its applications
description: scientific article; zbMATH DE number 166243