Some Studies On The Semiring Of Tropical Matrix

The theory of tropical matrix is one of the important contents in algebra-ic theory,which has been widely used in combinatorial optimisation,automate theory,control theory and many other important scientific fields.In this dis-sertation,we mainly studies some properities of tropical matrix semiring.The main results as follows:Firstly,by using equivalence transformation of tropical matrix,we discuss the block matrix of the matrix E,where E is a symmetric idempotent matrix and all main diagonal entries are O.Moreover,we study the centralizer of the matrix E,i.e.,the matrices which commute with E.Secondly,we introduce and study the Green's relations on the tropical ma-trix semigroup and prove that the Green's relations on (?)?0 and (?)?0 are inherited.In addition,we discuss some properities of normal tropical matrix.