On tropical supereigenvectors

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On tropical supereigenvectors. / Butkovic, Peter.

In: Linear Algebra and its Applications, Vol. 498, 06.2016, p. 574–591.

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@article{8a208c408d7d4cabaa55ecf4bc1eb23b,
title = "On tropical supereigenvectors",
abstract = "The task of finding tropical eigenvectors and subeigenvectors, that is non-trivial solutions to A⊗x=λ⊗x and A⊗x≤λ⊗x in the max-plus algebra, has been studied by many authors since the 1960s. In contrast the task of finding supereigenvectors, that is solutions to A⊗x≥λ⊗x, has attracted attention only recently. We present a number of properties of supereigenvectors focusing on a complete characterization of the values of λ associated with supereigenvectors and in particular finite supereigenvectors. The proof of the main statement is constructive and enables us to find a non-trivial subspace of finite supereigenvectors. We also present an overview of key related results on eigenvectors and subeigenvectors.",
keywords = "Matrix, Eigenvalue, Eigenvector, Subeigenvector, Supereigenvector",
author = "Peter Butkovic",
year = "2016",
month = jun,
doi = "10.1016/j.laa.2016.02.033",
language = "English",
volume = "498",
pages = "574–591",
journal = "Linear Algebra and its Applications",
issn = "0024-3795",
publisher = "Elsevier",

}

RIS

TY - JOUR

T1 - On tropical supereigenvectors

AU - Butkovic, Peter

PY - 2016/6

Y1 - 2016/6

N2 - The task of finding tropical eigenvectors and subeigenvectors, that is non-trivial solutions to A⊗x=λ⊗x and A⊗x≤λ⊗x in the max-plus algebra, has been studied by many authors since the 1960s. In contrast the task of finding supereigenvectors, that is solutions to A⊗x≥λ⊗x, has attracted attention only recently. We present a number of properties of supereigenvectors focusing on a complete characterization of the values of λ associated with supereigenvectors and in particular finite supereigenvectors. The proof of the main statement is constructive and enables us to find a non-trivial subspace of finite supereigenvectors. We also present an overview of key related results on eigenvectors and subeigenvectors.

AB - The task of finding tropical eigenvectors and subeigenvectors, that is non-trivial solutions to A⊗x=λ⊗x and A⊗x≤λ⊗x in the max-plus algebra, has been studied by many authors since the 1960s. In contrast the task of finding supereigenvectors, that is solutions to A⊗x≥λ⊗x, has attracted attention only recently. We present a number of properties of supereigenvectors focusing on a complete characterization of the values of λ associated with supereigenvectors and in particular finite supereigenvectors. The proof of the main statement is constructive and enables us to find a non-trivial subspace of finite supereigenvectors. We also present an overview of key related results on eigenvectors and subeigenvectors.

KW - Matrix

KW - Eigenvalue

KW - Eigenvector

KW - Subeigenvector

KW - Supereigenvector

U2 - 10.1016/j.laa.2016.02.033

DO - 10.1016/j.laa.2016.02.033

M3 - Article

VL - 498

SP - 574

EP - 591

JO - Linear Algebra and its Applications

JF - Linear Algebra and its Applications

SN - 0024-3795

ER -