Schur-like forms for matrix Lie groups, Lie algebras and Jordan algebras
type: Item
instance of: scholarly article
title: Schur-like forms for matrix Lie groups, Lie algebras and Jordan algebras
zbMATH Open document ID: 0959.17002
DOI: 10.1016/S0024-3795(98)10133-7
author: Christian Mehl
author: Volker Mehrmann
author: G. S. Ammar
published in: Linear Algebra and its Applications
publication date: 2000-03-08T00:00:00Z
review text: The paper deals with the matrix Lie groups \({\mathcal O}_{p,q}\) of \(\Sigma_{p,q}\)-unitary matrices and Lie group \(Sp(2n)\) of symplectic matrices. Here \(\Sigma_{p,q}= \left[ \begin{smallmatrix} -Ip &0\\ 0 &Ip \end{smallmatrix} \right]\). Lie and Jordan algebras associated with these groups are considered also. The authors describe structure-preserving similarity transformations to condensed forms for the matrices of the groups. These Schur-like forms, in general, are not diagonal or Schur ones, but display the eigenvalue of the matrices. Matrices in the associated Lie or Jordan algebras inherit the related forms under these transformations. The authors also consider the intersections of the above classes of matrices and present the Schur-like forms for multi-structured matrices that arise in quantum chemistry.
Mathematics Subject Classification ID: 17B05
Mathematics Subject Classification ID: 15B33
Mathematics Subject Classification ID: 15A18
Mathematics Subject Classification ID: 17C10
Mathematics Subject Classification ID: 22E10
zbMATH DE Number: 1331744
zbMATH Keywords: matrix Lie groups
zbMATH Keywords: similarity transformations
zbMATH Keywords: Schur-like forms
reviewed by: Alexander Rudy
MaRDI profile type: Publication
Wikidata QID: Q115339985
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full work available at URL: s0024-3795(98)10133-7
OpenAlex ID: W2082077121
description: scientific article; zbMATH DE number 1331744