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 |
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Pages (from-to) | 169-190 |
Journal | Linear Algebra and its Applications |
Volume | 507 |
Early online date | 8 Jun 2016 |
DOIs | |
Publication status | Published - 15 Oct 2016 |
Keywords
- Max algebra
- one-sided system
- weakly robust
- interval analysis