The Re-nonnegative definite solutions to the matrix equation $AXB=C$
Qing‐Wen Wang, Chang Lan Yang · Czech digital mathematics library · 1998
summary:An $n\times n$ complex matrix $A$ is called Re-nonnegative definite (Re-nnd) if the real part of $x^{\ast } Ax$ is nonnegative for every complex $n$-vector $x$. In this paper criteria for a partitioned matrix to be Re-nnd are given. A necessary and sufficient condition for the existence of and an expression for the Re-nnd solutions of the matrix equation $AXB=C$ are presented.