Qingwen Wang, Changlan Yang
The Re-nonnegative definite solutions to the matrix equation $AXB=C$

Comment.Math.Univ.Carolinae 39,1 (1998) 7-13.

Abstract: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.

Keywords: Re-nonnegative define matrix, matrix equation, generalized singular value decomposition
AMS Subject Classification: 15A24, 15A57