On the eigenproblem of matrices over distributive lattices.
type: Item
instance of: scholarly article
title: On the eigenproblem of matrices over distributive lattices.
zbMATH Open document ID: 1033.15005
DOI: 10.1016/S0024-3795(03)00550-0
published in: Linear Algebra and its Applications
publication date: 2003-11-19T00:00:00Z
review text: The author considers the eigenproblem for matrices over the class of complete and completely distributive lattices. He obtains the eigenvector of a given matrix \(A\) for a given eigenvalue \(l\), and gives some properties of the maximum matrix \(M(l,x)\) in \(T(l,x)\), the set of matrices with given eigenvector \(x\) and eigenvalue \(l\). Then he introduces the concept of primitive vectors and considers the structure of matrices which possess a given primitive eigenvector \(x\) and shows in particular that, for any given \(l \) in \(L\), there is a matrix, namely \(M(l,x)\), having \(x\) as a maximal primitive eigenvector associated with the eigenvalue \(l\).
Mathematics Subject Classification ID: 15A18
Mathematics Subject Classification ID: 06D10
Mathematics Subject Classification ID: 15B33
zbMATH DE Number: 2005994
zbMATH Keywords: distributive lattice
zbMATH Keywords: matrix
zbMATH Keywords: eigenvalue
zbMATH Keywords: eigenvector
zbMATH Keywords: primitive eigenvector
author: Yijia Tan
reviewed by: Nicholas Karampetakis
MaRDI profile type: Publication
cites work: Q5529506
cites work: Eigenvectors in Bottleneck algebra
cites work: Monotone eigenspace structure in max-min algebra
cites work: Boolean spectral theory
cites work: Q5341813
cites work: Resolution of eigen fuzzy sets equations
cites work: Eigenvalues and eigenvectors for matrices over distributive lattices
description: scientific article; zbMATH DE number 2005994