Geometric proofs of some theorems of Schur-Horn type
type: Item
instance of: scholarly article
title: Geometric proofs of some theorems of Schur-Horn type
zbMATH Open document ID: 0948.15015
DOI: 10.1016/S0024-3795(98)10169-6
author: T. R. W. Richa
author: Ricardo S. Leite
author: Carlos Tomei
published in: Linear Algebra and its Applications
publication date: 2000-11-26T00:00:00Z
review text: New geometric proofs of some theorems in linear algebra are given. Firstly, the classical Schur-Horn theorem for real symmetric (resp. Hermitian) matrices is proved. Secondly, a less known Schur-Horn theorem for skew-symmetric matrices is proved by geometric methods. Standard symplectic arguments are used to obtain two complex counterparts of this theorem. It is emphasized that some elements of the authors' geometric proofs are familiar to the closely related subjects of Coxeter groups and Lie algebras; the authors' conclusion is that their results can be special cases of a more general theorem. Finally, the geometric techniques are used to prove Horn's characterization of the diagonal entries of orthogonal matrices.
reviewed by: Valeriu Prepeliţă
Mathematics Subject Classification ID: 15A42
Mathematics Subject Classification ID: 15A45
Mathematics Subject Classification ID: 15B57
zbMATH DE Number: 1331730
zbMATH Keywords: moment map
zbMATH Keywords: symmetric and skew-symmetric matrices
zbMATH Keywords: geometric proofs
zbMATH Keywords: Schur-Horn theorem
zbMATH Keywords: Coxeter groups
zbMATH Keywords: Lie algebras
zbMATH Keywords: orthogonal matrices
MaRDI profile type: Publication
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Wikidata QID: Q127846210
description: scientific article; zbMATH DE number 1331730