Covariant bi-differential operators on matrix space

A family of bi-differential operators from $C^\infty\big(\Mat(m,\mathbb R)\times\Mat(m,\mathbb R)\big)$ into $C^\infty\big(\Mat(m,\mathbb R)\big)$ which are covariant for the projective action of the group $SL(2m,\mathbb R)$ on $\Mat(m,\mathbb R)$ is constructed, generalizing both the \emph{transvectants} and the \emph{Rankin-Cohen brackets} (case $m=1$).