A counterexample to a conjecture of Friedland
type: Item
instance of: scholarly article
title: A counterexample to a conjecture of Friedland
zbMATH Open document ID: 1165.15011
author: Wei Wang
published in: Linear Algebra and its Applications
publication date: 2009-04-29T00:00:00Z
review text: The author studies a conjecture of \textit{S. Friedland} [Linear Algebra Appl. 192, 109--114 (1993; Zbl 0787.15011)] which says that ``if two symmetric matrices over the ring of integers are orthogonally similar over both the field of rationals and the ring of \(p\)-adic integers, then the two symmetric matrices should be orthogonally similar over the ring of integers''. A clever method for constructing counterexamples to the conjecture is provided. An explicit example is also given. Finally, the paper presents a modified version of the conjecture above, i.e., requiring that the characteristic polynomial of the matrices being irreducible over \(Q[x]\). The paper is well written and very readable.
Mathematics Subject Classification ID: 15A21
zbMATH DE Number: 5549258
zbMATH Keywords: rational orthogonal similarity
zbMATH Keywords: \(p\)-adic numbers
zbMATH Keywords: counterexamples
reviewed by: Chen Sheng
MaRDI profile type: Publication
full work available at URL: j.laa.2008.11.009
OpenAlex ID: W1967351911
Wikidata QID: Q122951855
cites work: Q4298518
cites work: Quadratic forms and the graph isomorphism problem
cites work: Rational orthogonal similarity of rational symmetric matrices
cites work: Orthogonal similarity and pairs of quadratic forms
cites work: Some results on the spectral reconstruction problem
DOI: 10.1016/J.LAA.2008.11.009
description: scientific article; zbMATH DE number 5549258