## 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

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