The solvability conditions for the inverse eigenvalue problem of the symmetrizable matrices.
type: Item
instance of: scholarly article
title: The solvability conditions for the inverse eigenvalue problem of the symmetrizable matrices.
zbMATH Open document ID: 1052.15010
author: Xiyan Hu
author: Lei Zhang
author: Yuanbei Deng
published in: Journal of Computational and Applied Mathematics
publication date: 2004-03-14T00:00:00Z
review text: The authors investigate the inverse eigenvalue problem of finding a symmetrizable real matrix \(A\) that solves \(AX = X\Lambda\) for a given real matrix \(X\) and a given real diagonal matrix \(\Lambda\), as well as a related minimal norm approximation problem. The solution is found via the singular value decomposition (SVD) of a related matrix. Despite the paper's short and recent list of references, symmetrizable matrices have been studied for several centuries by Cauchy, Weierstraß, Kronecker, Frobenius, Taussky, Zassenhaus, Thompson among others, as well as by the reviewer. The basic theorems and lemmas of p. 102 are all well known and need no proof. One (Lemma 2.1) is erroneously attributed to a 1991 book in Chinese, while the SVD is laughably attributed to Golub and van Loan. These are unforgivable lapses of the Journal's editorial system. The authors' work is otherwise nice and deserved better editorial attention and care.
Mathematics Subject Classification ID: 15A29
Mathematics Subject Classification ID: 15B57
Mathematics Subject Classification ID: 15A18
Mathematics Subject Classification ID: 15A24
Mathematics Subject Classification ID: 15A21
zbMATH DE Number: 2055538
zbMATH Keywords: symmetrizable matrix
zbMATH Keywords: inverse eigenvalue problem
zbMATH Keywords: optimal approximation
zbMATH Keywords: matrix norm
reviewed by: Frank Uhlig
MaRDI profile type: Publication
full work available at URL: j.cam.2003.08.056
OpenAlex ID: W2045892986
cites work: Q5185900
cites work: Q3804078
cites work: Q5203165
DOI: 10.1016/J.CAM.2003.08.056
description: scientific article; zbMATH DE number 2055538