Geometric characterization and classification of marked subspaces
type: Item
instance of: scholarly article
title: Geometric characterization and classification of marked subspaces
zbMATH Open document ID: 0852.15007
DOI: 10.1016/0024-3795(94)00107-3
author: Josep Ferrer
author: Ferran Puerta
author: Xavier Puerta
published in: Linear Algebra and its Applications
publication date: 1996-06-10T00:00:00Z
review text: Let \(f\) be a linear endomorphism of a finite-dimensional \(\mathbb{C}\)-vector space \(E\). An \(f\)-invariant subspace \(W \subset E\) is said to be marked, if there exists a Jordan basis of \(f \mid W\) which can be extended to a Jordan basis of \(f\). [See also \textit{R. Bru}, \textit{L. Rodman} and \textit{H. Schneider}, Linear Algebra Appl. 150, 209-225 (1991; Zbl 0726.15005)]. The authors give a characterization and a classification of marked subspaces \(W\) of \(E\) in terms of \(W\) and the family of subspaces \(\ker f^h \cap \text{im} f^d\). However, the details are too involved to be stated here.
reviewed by: Hans Havlicek
Mathematics Subject Classification ID: 15A21
Mathematics Subject Classification ID: 15A18
Mathematics Subject Classification ID: 15A03
zbMATH DE Number: 871108
zbMATH Keywords: invariant subspace
zbMATH Keywords: geometric characterization
zbMATH Keywords: Jordan basis
zbMATH Keywords: classification
zbMATH Keywords: marked subspaces
MaRDI profile type: Publication
full work available at URL: 0024-3795(94)00107-3
OpenAlex ID: W2027503680
cites work: Extensions of Jordan bases for invariant subspaces of a matrix
cites work: Q3748420
description: scientific article; zbMATH DE number 871108