The common invariant subspace problem: an approach via Gröbner bases
type: Item
instance of: scholarly article
title: The common invariant subspace problem: an approach via Gröbner bases
zbMATH Open document ID: 1067.15002
author: Donu Arapura
author: Chris Peterson
published in: Linear Algebra and its Applications
publication date: 2004-08-06T00:00:00Z
review text: The authors show how the problem of existence of a common eigenvector for a given finite set of \(n\times n\) matrices can be formulated in the language of affine varieties via Gröbner bases. No proofs are given. Instead of the proof a sketch of the algorithm for determining the number of maximal common eigenspaces of a given dimension is presented.
Mathematics Subject Classification ID: 15A18
Mathematics Subject Classification ID: 13P10
zbMATH DE Number: 2083488
zbMATH Keywords: Eigenvector
zbMATH Keywords: Invariant subspace
zbMATH Keywords: Grassmann variety
zbMATH Keywords: Gröbner basis
zbMATH Keywords: Algorithm
reviewed by: Witold Więsław
MaRDI profile type: Publication
full work available at URL: j.laa.2003.03.001
OpenAlex ID: W2022716134
cites work: Solving the two-dimensional CIS problem by a rational algorithm
cites work: Q4023642
cites work: Direct methods for primary decomposition
cites work: Common invariant subspaces of two matrices
cites work: Q4002797
cites work: Common eigenvectors of two matrices
cites work: A criterion for the existence of common invariant subspaces of matrices
DOI: 10.1016/J.LAA.2003.03.001
description: scientific article; zbMATH DE number 2083488