Several Researches Of Linear Transformations On Semilinear Spaces

Semilinear spaces over a semiring are one of the important research con-tents of linear algebra,and the linear transformation is an useful tool for s-tudying semilinear spaces.This dissertation explores some properties of linear transformations in semilinear spaces and invertible linear operators that pre-serve elements commutative in matrix spaces over a class of semirings.The main results are as follows:1.We explore linear transformations in semilinear spaces over a commu-tative semiring,and give some properties of the linear transformation and its image and kernel.2.We define similar linear transformations,and give the necessary and sufficient conditions for the similarity of linear transformation in-semilinear space(1₉)over a class of zerosumfree semirings.3.We discuss invertible linear operators that preserve commuting pairs of matrices over commutative entire antiring and its arbitrary direct product.Furthermore,the relationship between invertible linear operators that preserve commuting pairs of matrices and invertible linear operators that preserve{1}-inverses of matrices over a class of commutative entire antiring are revealed.