Bounds for eigenvalues using the trace and determinant
type: Item
instance of: scholarly article
title: Bounds for eigenvalues using the trace and determinant
zbMATH Open document ID: 0885.15011
DOI: 10.1016/S0024-3795(97)00067-0
author: Jorma K. Merikoski
author: Ari Virtanen
published in: Linear Algebra and its Applications
publication date: 1997-10-20T00:00:00Z
review text: The authors consider a square matrix of order \(n\) with real positive eigenvalues \(\lambda_1\geq\cdots\geq \lambda_n>0\) and get lower and upper bounds for products \(\lambda_k\cdot\cdots\cdot \lambda_l\) and sums \(\lambda_k+\cdots+ \lambda_l\) of eigenvalues by using the trace and the determinant as well as of the numbers \(n\), \(k\) and \(l\). In some cases bounds of \textit{H. Wolkowicz} and \textit{G. P. H. Styan} [ibid. 29, 471-506 (1980; Zbl 0435.15015)] could be improved.
Mathematics Subject Classification ID: 15A42
zbMATH DE Number: 1076284
zbMATH Keywords: eigenvalues
zbMATH Keywords: bounds
zbMATH Keywords: trace
zbMATH Keywords: determinant
MaRDI profile type: Publication
cites work: A Simple Estimate of the Condition Number of a Linear System
cites work: A best upper bound for the 2-norm condition number of a matrix
cites work: Bounds for eigenvalues using traces
description: scientific article; zbMATH DE number 1076284