Estimates of the determinant of a perturbed identity matrix
type: Item
instance of: scholarly article
title: Estimates of the determinant of a perturbed identity matrix
zbMATH Open document ID: 1403.15003
published in: Linear Algebra and its Applications
publication date: 2018-10-11T00:00:00Z
review text: The author presents bounds for the determinant of a real perturbation \(I + E\) of the identity matrix \(I\), depending on the trace \(\operatorname{tr}(E)\) of \(E\) and the Frobenius norm \(\varepsilon\) of the (real or complex) perturbation \(E\). It is assumed that the difference of the bounds is not larger than \(\varepsilon^2 + O(\varepsilon^3)\) provided that \(\varepsilon< 1\). Moreover, he proves a bound of order \(\varepsilon^2\) on the relative error between the above mentioned determinant and \(\exp({\operatorname{tr}}(E))\).
Mathematics Subject Classification ID: 15A15
Mathematics Subject Classification ID: 65F40
zbMATH DE Number: 6951560
zbMATH Keywords: determinant
zbMATH Keywords: Hadamard bound
zbMATH Keywords: Ostrowski bound
zbMATH Keywords: Hans-Schneider bound
zbMATH Keywords: perturbation of identity
author: Siegfried M. Rump
reviewed by: George Stoica
MaRDI profile type: Publication
full work available at URL: j.laa.2018.08.009
OpenAlex ID: W2886939563
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Wikidata QID: Q129383824
DOI: 10.1016/J.LAA.2018.08.009
describes a project that uses: Digital Library of Mathematical Functions
description: scientific article; zbMATH DE number 6951560