Weyl and Lidskiĭ inequalities for general hyperbolic polynomials
type: Item
instance of: scholarly article
title: Weyl and Lidskiĭ inequalities for general hyperbolic polynomials
zbMATH Open document ID: 1219.12001
author: Denis Serre
published in: Chinese Annals of Mathematics. Series B
publication date: 2010-01-04T00:00:00Z
review text: In this paper the author focuses on some linear inequalities satisfied by the roots of hyperbolic polynomials (and by eigenvalues of Hermitian matrices as well). The whole set of such inequalities was first supposed to be true for the case of Hermitian matrices by \textit{A. Horn} [Pac. J. Math. 12, 225--241 (1962; Zbl 0112.01501)]. Horn's conjecture was later proved with some advanced tools, such as actions of Lie groups, Schubert calculus and representations of the group \(U(n)\). The author proposes a new proof for a part of Horn's inequalities, the so-called Weyl and Lidskiĭ ones. This proof is elementary and elegant, it relies on a combinatorial criterion and it is free from representation theory and Schubert calculus arguments, as well as the theory of hyperbolic partial differential equations.
reviewed by: Cristina Bertone
Mathematics Subject Classification ID: 12D10
Mathematics Subject Classification ID: 26C10
zbMATH DE Number: 5652266
zbMATH Keywords: hyperbolic polynomials
zbMATH Keywords: real roots
zbMATH Keywords: eigenvalues of Hermitian matrices
MaRDI profile type: Publication
full work available at URL: s11401-009-0169-3
OpenAlex ID: W2050063691
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DOI: 10.1007/S11401-009-0169-3
description: scientific article; zbMATH DE number 5652266