Paper Info
Title
The Spectra Of Reducible Matrices Over Complete Commutative Idempotent Semifields And Their Spectral Lattices
Abstract
Previous work has shown a relation between L-valued extensions of Formal Concept Analysis and the spectra of some matrices related to L-valued contexts. To clarify this relation, we investigated elsewhere the nature of the spectra of irreducible matrices over idempotent semifields in the framework of dioids, naturally ordered semirings, that encompass several of those extensions. This initial work already showed many differences with respect to their counterparts over incomplete idempotent semifields, in what concerns the definition of the spectrum and the eigenvectors. Considering special sets of eigenvectors also brought out complete lattices in the picture and we argue that such structure may be more important than standard eigenspace structure for matrices over completed idempotent semifields. In this paper, we complete that investigation in the sense that we consider the spectra of reducible matrices over completed idempotent semifields and dioids, giving, as a result, a constructive solution to the all-eigenvectors problem in this setting. This solution shows that the relation of complete lattices to eigenspaces is even tighter than suspected.
Year
DOI
Venue
2016
10.1080/03081079.2015.1072923
INTERNATIONAL JOURNAL OF GENERAL SYSTEMS
Keywords
Field
DocType
Dioids, complete idempotent semifields, all-eigenvectors problem, spectral order lattices, eigenlattices
Discrete mathematics,Algebra,Lattice (order),Commutative property,Matrix (mathematics),Constructive,Idempotence,Formal concept analysis,Mathematics,Idempotent matrix,Eigenvalues and eigenvectors
Journal
Volume
Issue
ISSN
45
2
0308-1079
Citations 
PageRank 
References 
1
0.36
7
Authors
2
Name
Order
Citations
PageRank
Francisco J. Valverde-Albacete111620.84
Carmen Peláez-moreno213022.07