Characterization of invariant spaces under a symmetric real matrix and its permutations
type: Item
instance of: scholarly article
title: Characterization of invariant spaces under a symmetric real matrix and its permutations
zbMATH Open document ID: 0712.15003
DOI: 10.1016/0024-3795(90)90358-J
author: Ching-Shui Cheng
author: Ker-Chau Li
published in: Linear Algebra and its Applications
publication date: 1990-01-01T00:00:00Z
review text: The authors solve the following two closely related problems: (1) given is a real symmetric matrix W of order n; find the subspaces of \(R^ n\) invariant for all the matrices \(\pi^ TW\pi\), where \(\pi\) runs over all n! permutation matrices; (2) given is a subspace \(V\subset R^ n\); find all real symmetric matrices W such that V would be invariant for all matrices \(\pi^ TW\pi.\) For most of W the problem (1) has only trivial solutions \(\{\) \(0\}\) and \(\{R^ n\}\). The authors find all matrices W for which there exist nontrivial solutions of the problem (1) and give an explicit description of the set \(\{\) \(W\}\) for any nontrivial V in the problem (2).
Mathematics Subject Classification ID: 15A04
Mathematics Subject Classification ID: 15A18
zbMATH DE Number: 4171109
zbMATH Keywords: invariant subspaces
zbMATH Keywords: symmetric matrix
reviewed by: Boris Raykhshteyn
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 4171109