The characteristic subspace lattice of a linear transformation
type: Item
instance of: scholarly article
title: The characteristic subspace lattice of a linear transformation
zbMATH Open document ID: 1368.15002
author: David Mingueza
author: M. Eulalia Montoro
author: A. Roca
published in: Linear Algebra and its Applications
publication date: 2016-08-17T00:00:00Z
full work available at URL: http://hdl.handle.net/10251/151298
review text: In this paper, the authors analyze basic properties of the lattice of the characteristic subspaces \(\mathrm{Chinv}(J)\) based on a nilpotent Jordan matrix \(J\) for the field \(\mathrm{GF}(2)\). \(\mathrm{Chinv}(J)\) is a lattice with inclusion as order, intersection as meet and linear sum as join. Assuming the Shoda condition for a nilpotent Jordan matrix \(J\), it is shown that \(\mathrm{Chinv}(J)\) is not distributive, but it is modular. Moreover, it is not complemented but finite. At the end, the authors show that \(\mathrm{Chinv}(J)\) is a sublattice of \(\mathrm{Inv}(J)\) (the invariant subspaces) and that there is an anti-isomorphism from \(\mathrm{Chinv}(J)\) to \(\mathrm{Chinv}(J)\). Hence, the considered lattice is self-dual.
Mathematics Subject Classification ID: 15A03
Mathematics Subject Classification ID: 47A15
Mathematics Subject Classification ID: 06C10
Mathematics Subject Classification ID: 06D50
zbMATH DE Number: 6617593
zbMATH Keywords: hyperinvariant subspaces
zbMATH Keywords: characteristic subspaces
zbMATH Keywords: lattices
reviewed by: Barbara Pekala
MaRDI profile type: Publication
OpenAlex ID: W2419189574
cites work: Hyperinvariant, characteristic and marked subspaces
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cites work: Q3748420
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cites work: Description of characteristic non-hyperinvariant subspaces over the field \(GF(2)\)
DOI: 10.1016/J.LAA.2016.06.003
description: scientific article; zbMATH DE number 6617593