Geodesic
The Re-nonnegative definite solutions to the matrix equation $AXB=C$
Commentationes Mathematicae Universitatis Carolinae, Tome 39 (1998) no. 1, pp. 7-13

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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.
Classification : 15A24, 15A57
Keywords: Re-nonnegative define matrix; matrix equation; generalized singular value decomposition 
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     title = {The {Re-nonnegative} definite solutions to the matrix equation $AXB=C$},
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Wang, Qingwen; Yang, Changlan. The Re-nonnegative definite solutions to the matrix equation $AXB=C$. Commentationes Mathematicae Universitatis Carolinae, Tome 39 (1998) no. 1, pp. 7-13. http://geodesic.mathdoc.fr/item/CMUC_1998__39_1_a1/