On positive definite preserving linear transformations of rank $r$ on real symmetric matrices

Doan The Hieu, Huynh Dinh Tuan

We study on what conditions on $B_k,$ \ a linear transformation of rank $r$ \label{form} T(A)=\sum_{k=1}^r\tr(AB_k)U_k where $U_k,k=1,2,...,r$ are linear independent and all pos…