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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.
Original language | English |
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Pages (from-to) | 574–591 |
Journal | Linear Algebra and its Applications |
Volume | 498 |
Early online date | 3 Mar 2016 |
DOIs | |
Publication status | Published - Jun 2016 |
Keywords
- Matrix
- Eigenvalue
- Eigenvector
- Subeigenvector
- Supereigenvector
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- 1 Finished
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Perron-Frobenius Theory and Max-Algebraic Combinatorics of Nonnegative Matrices
Butkovic, P.
Engineering & Physical Science Research Council
12/03/12 → 11/03/14
Project: Research Councils