Extending CSR Decomposition to Tropical Inhomogeneous Matrix Products

TL;DR

This paper extends the CSR decomposition method from tropical matrix powers to inhomogeneous matrix products, providing conditions for its applicability and demonstrating limitations with counterexamples.

Contribution

It introduces CSR terms for inhomogeneous products and establishes bounds for when the decomposition is possible, expanding the theoretical framework.

Findings

CSR decomposition can be extended to certain inhomogeneous products

Bounds on the length for CSR decomposition are provided

Counterexamples show limitations of the method

Abstract

This article presents an attempt to extend the CSR decomposition, previously introduced for tropical matrix powers, to tropical inhomogeneous matrix products. The CSR terms for inhomogeneous matrix products are introduced, then a case is described where an inhomogeneous product admits such CSR decomposition after some length and give a bound on this length. In the last part of the paper a number of counterexamples are presented to show that inhomogeneous products do not admit CSR decomposition under more general conditions.