On the powers of matrices in bottleneck/fuzzy algebra Original Research Article

Powers of square matrices under the operations asterisk in circle = max and circle times operator = min are studied. We show that the powers of a given matrix stabilize if and only if its orbits stabilize for each starting vector and prove a necessary and sufficient condition for this property using the associated graphs of the matrix. Applications of the obtained results to several special classes of matrices (including circulants) are given.