A characterization of matrix groups that act transitively on the cone of positive definite matrices
type: Item
instance of: scholarly article
title: A characterization of matrix groups that act transitively on the cone of positive definite matrices
zbMATH Open document ID: 0798.15016
DOI: 10.1016/0024-3795(94)90347-6
author: Steen A. Andersson
author: Michael D. Perlman
published in: Linear Algebra and its Applications
publication date: 1994-06-09T00:00:00Z
review text: It is well known that the group of all nonsingular lower block-triangular \(p\times p\) matrices acts transitively on the cone \({\mathcal P}^*\) of all positive definite \(p \times p\) matrices. In this paper the converse is established: If a matrix group acts transitively on \({\mathcal P}^*\), then its group algebra must be (similar to) the algebra of all lower block- triangular \(p \times p\) matrices with respect to a fixed partitioning.
Mathematics Subject Classification ID: 15A30
zbMATH DE Number: 566096
zbMATH Keywords: cone of positive definite matrices
zbMATH Keywords: matrix group
zbMATH Keywords: group algebra
reviewed by: Rodica Covaci
MaRDI profile type: Publication
full work available at URL: 0024-3795(94)90347-6
OpenAlex ID: W2044312103
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description: scientific article; zbMATH DE number 566096