Decomposability and structure of nonnegative bands in \({\mathcal M}_n(\mathbb{R})\)
type: Item
instance of: scholarly article
title: Decomposability and structure of nonnegative bands in \({\mathcal M}_n(\mathbb{R})\)
zbMATH Open document ID: 0932.15008
DOI: 10.1016/S0024-3795(98)10233-1
author: Alka Marwaha
published in: Linear Algebra and its Applications
publication date: 2000-03-13T00:00:00Z
review text: A standard subspace of \(\mathbb{R}^n\) is a space spanned by a subset of the standard basis \(\{e_1,e_2,\dots,e_n\}\). A multiplicative semigroup \(S\) in \(M_n(\mathbb{R})\) is said to be decomposable if its members have a common nontrivial standard invariant subspace. Necessary and sufficient conditions for decomposability of nonnegative semigroups are given. In particular, decomposability of nonnegative bands (semigroups of idempotents) and their structure is discussed. It is proved that a nonnegative band with each member having rank greater than 1 is decomposable. Also, a geometric characterization of maximal, rank-one nonnegative bands is given.
Mathematics Subject Classification ID: 15A30
zbMATH DE Number: 1331316
zbMATH Keywords: semigroups of idempotents
zbMATH Keywords: invariant subspace
zbMATH Keywords: decomposability
zbMATH Keywords: nonnegative bands
zbMATH Keywords: rank
reviewed by: Rodica Covaci
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 1331316