X-simple image eigencones of tropical matrices
Jan Plavka, Sergei Sergeev

TL;DR
This paper studies the structure of eigencones in tropical algebra, characterizing matrices with unique eigenvector solutions within intervals, and provides practical criteria for identifying such matrices.
Contribution
It introduces the concept of X-simple image eigencones in tropical matrices and offers geometric and combinatorial characterizations along with efficient checking criteria.
Findings
Characterization of matrices with X-simple image eigencones
Geometric and combinatorial descriptions provided
Efficient criteria for special cases derived
Abstract
We investigate max-algebraic (tropical) one-sided systems where is an eigenvector and lies in an interval . A matrix is said to have -simple image eigencone associated with an eigenvalue , if any eigenvector associated with and belonging to the interval is the unique solution of the system in . We characterize matrices with -simple image eigencone geometrically and combinatorially, and for some special cases, derive criteria that can be efficiently checked in practice.
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