# Solving Linear Systems over Tropical Semirings through Normalization Method and its Applications

## TL;DR

This paper presents a normalization technique for solving linear systems over tropical semirings, enabling solution determination, rank computation, and degrees of freedom analysis, with practical flowchart applications.

## Contribution

It introduces a novel normalization method for tropical linear systems, providing tools for solution finding, rank analysis, and degrees of freedom assessment.

## Key findings

- The normalization method effectively solves tropical linear systems.
- It can determine the system's degrees of freedom.
- The method computes column and row ranks of matrices.

## Abstract

In this paper, we introduce and analyze a normalization method for solving a system of linear equations over tropical semirings. We use a normalization method to construct an associated normalized matrix, which gives a technique for solving the system. If solutions exist, the method can also determine the degrees of freedom of the system. Moreover, we present a procedure to determine the column rank and the row rank of a matrix. Flowcharts for this normalization method and its applications are included as well.