Maps Preserving Adjoint On Matrix Spaces

The problems to characterize the linear operators which preserve certain functions,subsets, relations and transformations invariants on matrix sets are called"LinearPreserver Problems". Linear Preserver Problem is a very active topic in the field ofmatrix theory, it has wide applications in other areas, such as, di?erential equations,systems control, etc. In the recent years, the study on the Linear Preserver Problem hasmade great progress.With Linear Preserver Problems maturing,many mathematiciansbegan to weaken or change the conditions to get more general results.E?ected by thisidea, we study the maps preserving adjoint matrix in the absence of additional on twomatrix spaces.After introducing the background and development of the Linear Preserver Prob-lem, we study the preserver problems on triangular matrix spaces and alternate matrixspaces over fields. The main results obtained in this thesis are as follows:1. We characterize the maps preserving adjoint matrix on triangle matrix spacesover fields.2. We characterize the maps preserving adjoint matrix on alternate matrix spacesover fields.