The structure of the eigenvectors of sparse matrices
type: Item
instance of: scholarly article
title: The structure of the eigenvectors of sparse matrices
zbMATH Open document ID: 0807.15006
DOI: 10.1016/0024-3795(94)90001-9
author: Walter F. Mascarenhas
published in: Linear Algebra and its Applications
publication date: 1994-09-26T00:00:00Z
full work available at URL: http://purl.umn.edu/1872
review text: The author shows that there exists a matrix \(B\) such that if \(\lambda\) is an eigenvalue of a matrix \(A\) with algebraic multiplicity \(m\), then there are \(m\) columns of \(B\) that form a basis for the maximal invariant subspace of \(A\) associated with \(\lambda\) and such that \(\text{struct} (B)\) (this is the usual directed graph associated with the zero-nonzero pattern of \(B)\) is a subgraph of the graph obtained by adding all the edges of the form \((i,i)\) to the transitive closure of \(\text{struct} (A)\).
Mathematics Subject Classification ID: 15A18
Mathematics Subject Classification ID: 15A21
Mathematics Subject Classification ID: 05C50
zbMATH DE Number: 644676
zbMATH Keywords: sparse matrices
zbMATH Keywords: eigenvectors
zbMATH Keywords: eigenvalue
zbMATH Keywords: invariant subspace
zbMATH Keywords: directed graph
reviewed by: Mihail Voicu
MaRDI profile type: Publication
OpenAlex ID: W2017406192
cites work: Predicting Structure in Sparse Matrix Computations
cites work: Q5789039
Wikidata QID: Q126780520
description: scientific article; zbMATH DE number 644676