Some remarks on a conjecture of de Oliveira
type: Item
instance of: scholarly article
title: Some remarks on a conjecture of de Oliveira
zbMATH Open document ID: 0658.15004
DOI: 10.1016/0024-3795(88)90327-8
author: Natalia Bebiano
author: João Da Providência
published in: Linear Algebra and its Applications
publication date: 1988-01-01T00:00:00Z
review text: Some years ago the present reviewer [Linear Multilinear Algebra 12, 153- 154 (1982)] conjectured that if A and B are normal matrices then the determinant of \(A+B\) lies in the convex hull of the complex numbers \(\prod_{i}(\alpha_ i+\beta_{\sigma (i)})\). Here the \(\alpha_ i's\) and the \(\beta_ i's\) are the eigenvalues of A and B respectively, and \(\sigma\) runs over the symmetric group of degree n. The authors prove that the conjecture is true in some particular cases as, for example, when \(| \alpha_ 1| =...=| \alpha_ n| =| \beta_ 1| =...=| \beta_ n|\).
Mathematics Subject Classification ID: 15A15
Mathematics Subject Classification ID: 15B57
zbMATH DE Number: 4075276
zbMATH Keywords: normal matrices
zbMATH Keywords: determinant
zbMATH Keywords: convex hull
zbMATH Keywords: eigenvalues
Wikidata QID: Q123252211
MaRDI profile type: Publication
full work available at URL: 0024-3795(88)90327-8
OpenAlex ID: W2051865765
cites work: The determinant of the sum of two normal matrices with prescribed eigenvalues
cites work: Bounds for the Determinant of the Sum of Hermitian Matrices
cites work: Matrices satisfying a conjecture of G. N. de Oliveira on determinants
description: scientific article; zbMATH DE number 4075276