Year: 2014
Type: preprint
Abstract: A matrix $A$ is said to have $X$-simple image eigenspace if any eigenvector $x$ belonging to the interval $X=\{x\colon \underline{x}\leq x\leq\overline{x}\}$ is the unique solution of the system $A\otimes y=x$ in $X$. The main result of this paper is a combinatorial characterization of such matrices in the linear algebra over max-min (fuzzy) semiring. The characterized property is related to and motivated by the general development of tropical linear algebra and interval analysis, as well as the notions of simple image set and weak robustness (or weak stability) that have been studied in max-min and max-plus algebras.
Source: arXiv (Cornell University)
Authors: Plavka, Jan, Sergeev, Sergei
Language: English
Topic: Advanced Algebra and Logic
Subfield: Computational Theory and Mathematics
Field: Computer Science
Domain: Physical Sciences
Open Access status: green
Award: G1807818597
OpenAlex ID: W2494078088