Linear Transformations Of Semilinear Spaces Over Commutative Semirings

This thesis mainly introduces the concepts of a linear transformation,an invert-ible transformation,an idempotent transformation and a nilpotent transformation,and defines the operations of transformations in semilinear spaces over commutative semirings.Then it discusses some properties of the invertible transformations and the idempotent transformations,respectively.It also shows some relationships between images and kernels of the linear transfor-mation.After that,this thesis defines the notions of an eigenvalue,an eigenvector,an invariant subspace and an eigensubspace of linear transformations,respectively,and obtains eigenvalues and eigenvectors of some special linear transformations.Finally,it shows some conclusions related to invariant subspaces and eigensubspaces of linear transformations,respectively.