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Keywords

Max algebra, Ultimate periodicity, Perron-Frobenius, Eigenspace, Core.

Abstract

The max-algebraic core of a nonnegative matrix is the intersection of column spans of all max-algebraic matrix powers. This paper investigates the action of a matrix on its core. Being closely related to ultimate periodicity of matrix powers, this study leads to new modifications and geometric characterizations of robust, orbit periodic and weakly stable matrices

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