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Description of characteristic non-hyperinvariant subspaces over the field GF(2)

Author
Mingueza, D.; Montoro, M.; Pacha, Juan R
Type of activity
Journal article
Journal
Linear algebra and its applications
Date of publication
2013-10-26
Volume
439
Number
12
First page
3734
Last page
3745
DOI
https://doi.org/10.1016/j.laa.2013.10.025 Open in new window
Repository
http://hdl.handle.net/2117/21028 Open in new window
URL
http://authors.elsevier.com/sd/article/S0024379513006599 Open in new window
Abstract
Given a square matrix A, an A-invariant subspace is called hyperinvariant (respectively, characteristic) if and only if it is also invariant for all matrices T (respectively, nonsingular matrices T) that commute with A. Shoda's Theorem gives a necessary and sufficient condition for the existence of characteristic non-hyperinvariant subspaces for a nilpotent matrix in GF(2). Here we present an explicit construction for all subspaces of this type. Given a square matrix A, an A-invariant subspace i...
Citation
Mingueza, D.; Montoro, M.; Pacha, J. Description of characteristic non-hyperinvariant subspaces over the field GF(2). "Linear algebra and its applications", 26 Octubre 2013, vol. 439, núm. 12, p. 3734-3745.
Keywords
Characteristic subspaces, Hyperinvariant subspaces, Shoda's Theorem
Group of research
SD - UPC Dynamical Systems

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