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.
|Journal||Linear Algebra and its Applications|
|Early online date||8 Jun 2016|
|Publication status||Published - 15 Oct 2016|
- Max algebra
- one-sided system
- weakly robust
- interval analysis