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The Re-nonnegative definite solutions to the matrix equation $A X B = C$

Qing Wen Wang; Chang Lan Yang — 1998

Commentationes Mathematicae Universitatis Carolinae

An $n \times n$ complex matrix $A$ is called Re-nonnegative definite (Re-nnd) if the real part of $x^{*} A x$ 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 $A X B = C$ are presented.

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The Re-nonnegative definite solutions to the matrix equation A X B = C

The Re-nonnegative definite solutions to the matrix equation $A X B = C$