Improving the localization of eigenvalues for complex matrices
type: Item
instance of: scholarly article
zbMATH Open document ID: 1247.15016
author: P. Sargolzaei
author: R. Rakhshanipur
publication date: 2012-07-11T00:00:00Z
full work available at URL: index.html
Mathematics Subject Classification ID: 15A42
zbMATH DE Number: 6054566
zbMATH Keywords: eigenvalues
zbMATH Keywords: spectrum
zbMATH Keywords: localization
zbMATH Keywords: rectangular regions
MaRDI profile type: Publication
title: Improving the localization of eigenvalues for complex matrices
published in: Applied Mathematical Sciences (Ruse)
review text: Let \(\lambda_i, i= 1,\dots,n\) denote the spectrum of a complex \(n\)-by-\(n\) matrix \(A\). Several well-known bounds for \(\sum|\lambda_i|^2\) in terms of \(\mathrm{tr}(A), \|A\|, \|AA^*-A^*A\|\) are stated. Generalizations to \(\mathrm{Re}(A)\) and \(\mathrm{Im}(A)\) lead to rectangles containing the spectrum of \(A\). Two examples of order 3 are given.
reviewed by: Ludwig Elsner
description: scientific article; zbMATH DE number 6054566