X-simplicity of interval max-min matrices

Title:

X-simplicity of interval max-min matrices

Creator:

Berežný, Štefan and Plavka, Ján

Identifier:

https://cdk.lib.cas.cz/client/handle/uuid:7e261f2e-340f-4604-bb1c-360f3317ca0e
uuid:7e261f2e-340f-4604-bb1c-360f3317ca0e
doi:10.14736/kyb-2018-3-0413

Subject:

max-min algebra, interval, eigenspace, and simple image set

Type:

model:article and TEXT

Format:

bez média and svazek

Description:

A matrix A is said to have \mbox{\boldmathX}-simple image eigenspace if any eigenvector x belonging to the interval \boldmathX={x:x−−≤x≤x¯¯¯} containing a constant vector is the unique solution of the system A⊗y=x in \mbox{\boldmathX}. The main result of this paper is an extension of \mbox{\boldmathX}-simplicity to interval max-min matrix \boldmathA={A:A−−≤A≤A¯¯¯¯} distinguishing two possibilities, that at least one matrix or all matrices from a given interval have \mbox{\boldmathX}-simple image eigenspace. \mbox{\boldmathX}-simplicity of interval matrices in max-min algebra are studied and equivalent conditions for interval matrices which have \mbox{\boldmathX}-simple image eigenspace are presented. The characterized property is related to and motivated by the general development of tropical linear algebra and interval analysis, as well as the notions of simple image set and weak robustness (or weak stability) that have been studied in max-min and max-plus algebras.

Language:

English

Rights:

http://creativecommons.org/publicdomain/mark/1.0/
policy:public

Source:

Kybernetika | 2018 Volume:54 | Number:3

Harvested from:

CDK

Metadata only:

false