Canonical forms of pairs of complex matrices
type: Item
instance of: scholarly article
title: Canonical forms of pairs of complex matrices
zbMATH Open document ID: 0717.15009
DOI: 10.1016/0024-3795(91)90240-W
author: Vlastimil Dlab
author: Claus Michael Ringel
published in: Linear Algebra and its Applications
publication date: 1991-01-01T00:00:00Z
review text: Representation theory of finite-dimensional associative algebras is used in order to classify explicitely the pairs of real subspaces of a finite- dimensional complex vector space in terms of complex matrices. In this respect one classifies the orbits of the direct product \(GL(m,{\mathbb{C}})\times GL(m_ 1,{\mathbb{R}})\times GL(m_ 2,{\mathbb{R}})\) acting on the set of pairs of \(m\times m_ i\) complex matrices \(A_ i\), \(i=1,2\), by \((A_ 1,A_ 2)(Q,P_ 1,P_ 2)=(QA_ 1P_ 1^{-1},QA_ 2P_ 2^{-1}).\) As a special case one resolves the general case of canonical forms of pairs of complex matrices.
reviewed by: Mihail Voicu
Mathematics Subject Classification ID: 15A21
zbMATH DE Number: 4181526
zbMATH Keywords: Representation theory
zbMATH Keywords: finite-dimensional associative algebras
zbMATH Keywords: pairs of real subspaces
zbMATH Keywords: orbits
zbMATH Keywords: canonical forms
zbMATH Keywords: pairs of complex matrices
MaRDI profile type: Publication
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full work available at URL: 0024-3795(91)90240-w
OpenAlex ID: W2076623680
description: scientific article; zbMATH DE number 4181526