Solving linear systems over tropical semirings through normalization method and its applications
Fateme Olia, Shaban Ghalandarzadeh, Amirhossein Amiraslani, Sedighe Jamshidvand · Journal of Algebra and Its Applications · 2020
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.