Linear preservers on Hessenberg matrices

Abstract

In this research, we focus on studying rank-1 preservers on Hessenberg matrices. The first purpose is to characterize linear maps preserving rank one. This result leads to attain the pattern of linear maps preserving determinants which is another purpose. Moreover, the form of linear maps preserving eigenvalues is given. Finally, on the same space, a characterization of surjective additive maps preserving rank one is provided.