The S-nilpotent Set Of Matrices And The Determinant Rank Of Matrices Over Commutative Semirings

This thesis mainly focuses on the simutaneously nilpotent set of matrices and the determinant rank of matrices over commutative semirings.Firstly,we discuss the relationship between a nilpotent matrix and the positive and negative parts of determinants,and give some necessary and sufficient conditions for the existence of finite simutaneously nilpotent matrix set;Then,some properties and relations between the determinant rank of matrix and positive and negative composite matrices are discussed;Finally,we give some conclusions about the determinant rank of a matrix and its generalized inverse matrix,and show some necessary and sufficient conditions for the existence of g-inverse,M-P inverse and group inverse of matrix with determinant rank one.