Linear spaces and preservers of bounded rank-two per-symmetric triangular matrices

Let F be a field and m,n be integers m,n > 3. Let SMn(F) and STn(F) denote the linear space of n × n per-symmetric matrices over F and the linear space of n × n per-symmetric triangular matrices over F, respectively. In this note, the structure of spaces of bounded rank-two matrices of STn(F) is determined. Using this structural result, a classification of bounded rank-two linear preservers ψ : STn(F) → SMm(F), with F of characteristic not two, is obtained. As a corollary, a complete description of bounded rank-two linear preservers between per-symmetric triangular matrix spaces over a field of characteristic not two is addressed.