On the max-algebraic core of a nonnegative matrix

TL;DR

This paper explores the max-algebraic core of nonnegative matrices, examining how matrices act on their cores and providing new geometric characterizations of various matrix classes related to periodicity and stability.

Contribution

It introduces new modifications and geometric characterizations of robust, orbit periodic, and weakly stable matrices in the context of max-algebraic matrix powers.

Findings

Characterizes the max-algebraic core and its properties.

Provides new geometric insights into matrix periodicity and stability.

Links the core to matrix classes like robust and orbit periodic matrices.

Abstract

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