Self-similar flows
type: Item
instance of: scholarly article
title: Self-similar flows
zbMATH Open document ID: 0666.15008
DOI: 10.1016/0024-3795(83)90137-4
published in: Linear Algebra and its Applications
publication date: 1988-01-01T00:00:00Z
review text: The semi-similar flows studied in the paper arise from a matrix differential equation \(\dot B=[B,C]\) where \(C=C(t,B)\). The problem is related to the problem of FG-decomposition: if \({\mathcal F}\), \({\mathcal G}\) are two closed subgroups of the general linear group \(GL_ n(F)\) \((F=R\) or C) with \({\mathcal F}\cap {\mathcal G}=\{I\},\) express \(A\in GL_ n(P)\) as a product FG where \(F\in {\mathcal F}\), \(G\in {\mathcal G}\). FG-algorithm: starting from a given matrix \(A\in GL_ n(F)\), introduce the sequence: \(A_ 0=A,A_ 1,A_ 2,..\). as follows: \(A_ i=\bar F_{i+1}\bar G_{i+1},\) \(A_{i+1}=\bar G_{i+1}\bar F_{i+1}.\) There exists a continuous version of this algorithm. The authors consider flows associated with different \({\mathcal F}\) and \({\mathcal G}\), using some results from the theory of Lie groups and algebras.
Mathematics Subject Classification ID: 15A23
Mathematics Subject Classification ID: 15A18
Mathematics Subject Classification ID: 34A30
Mathematics Subject Classification ID: 37C10
Mathematics Subject Classification ID: 65F15
zbMATH DE Number: 4089724
zbMATH Keywords: semi-similar flows
zbMATH Keywords: matrix differential equation
zbMATH Keywords: FG-decomposition
author: David S. Watkins
author: Ludwig Elsner
reviewed by: Boris Raykhshteyn
MaRDI profile type: Publication
full work available at URL: 0024-3795(83)90137-4
OpenAlex ID: W2082325315
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description: scientific article; zbMATH DE number 4089724