  Given a matrix $A\in \R^{n\times n}$ and a tall rectangular matrix $B \in
\R^{n\times q}$, $q < n$, we consider the problem of making the pair $(A,B)$
dissipative, that is the determination of a {\it feedback} matrix $K \in
\R^{q\times n}$ such that the field of values of $A-B K$ lies in the left half
open complex plane. We review and expand classical results available in the
literature on the existence and parameterization of the class of dissipating
matrices, and we explore new matrix properties associated with the problem. In
addition, we discuss various computational strategies for approximating the
minimal Frobenius norm dissipating $K$.
