X-simple image eigencones of tropical matrices

Jan Plavka; Sergey Sergeev

doi:10.1016/j.laa.2016.06.013

X-simple image eigencones of tropical matrices

Jan Plavka
, Sergey Sergeev

Mathematics

Research output: Contribution to journal › Article › peer-review

2 Citations (Scopus)

202 Downloads (Pure)

Abstract

We investigate max-algebraic (tropical) one-sided systems A⊗x=b where b is an eigenvector and x lies in an interval X. A matrix A is said to have X-simple image eigencone associated with an eigenvalue λ, if any eigenvector x associated with λ and belonging to the interval X is the unique solution of the system A⊗y=λx in X. We characterize matrices with X-simple image eigencone geometrically and combinatorially, and for some special cases, derive criteria that can be efficiently checked in practice.

Original language	English
Pages (from-to)	169-190
Journal	Linear Algebra and its Applications
Volume	507
Early online date	8 Jun 2016
DOIs	https://doi.org/10.1016/j.laa.2016.06.013
Publication status	Published - 15 Oct 2016

Keywords

Max algebra
one-sided system
weakly robust
interval analysis

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Plavka_Sergeev_X_simple_image_Linear_Algebra_and_its_Applications_2016Accepted author manuscript, 382 KBLicence: Creative Commons: Attribution-NonCommercial-NoDerivs (CC BY-NC-ND)

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abstract = "We investigate max-algebraic (tropical) one-sided systems A⊗x=b where b is an eigenvector and x lies in an interval X. A matrix A is said to have X-simple image eigencone associated with an eigenvalue λ, if any eigenvector x associated with λ and belonging to the interval X is the unique solution of the system A⊗y=λx in X. We characterize matrices with X-simple image eigencone geometrically and combinatorially, and for some special cases, derive criteria that can be efficiently checked in practice.",

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AU - Plavka, Jan

AU - Sergeev, Sergey

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N2 - We investigate max-algebraic (tropical) one-sided systems A⊗x=b where b is an eigenvector and x lies in an interval X. A matrix A is said to have X-simple image eigencone associated with an eigenvalue λ, if any eigenvector x associated with λ and belonging to the interval X is the unique solution of the system A⊗y=λx in X. We characterize matrices with X-simple image eigencone geometrically and combinatorially, and for some special cases, derive criteria that can be efficiently checked in practice.

AB - We investigate max-algebraic (tropical) one-sided systems A⊗x=b where b is an eigenvector and x lies in an interval X. A matrix A is said to have X-simple image eigencone associated with an eigenvalue λ, if any eigenvector x associated with λ and belonging to the interval X is the unique solution of the system A⊗y=λx in X. We characterize matrices with X-simple image eigencone geometrically and combinatorially, and for some special cases, derive criteria that can be efficiently checked in practice.

KW - Max algebra

KW - one-sided system

KW - weakly robust

KW - interval analysis

U2 - 10.1016/j.laa.2016.06.013

DO - 10.1016/j.laa.2016.06.013

M3 - Article

SN - 0024-3795

VL - 507

SP - 169

EP - 190

JO - Linear Algebra and its Applications

JF - Linear Algebra and its Applications

ER -

X-simple image eigencones of tropical matrices

Abstract

Keywords

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