A unified treatment for the restricted solutions of the matrix equation $AXB=C$

Abstract

In this paper, the Hermitian, skew-Hermitian, Re-nonnegative definite, Re-positive definite, Re-nonnegative definite least-rank and Re-positive definite least-rank solutions of the matrix equation $AXB= C$ are considered. The necessary and sufficient condition for the existence of such type of solution to the equation is provided and the explicit expression of the general solution is also given.

Keywords

• matrix equation
• hermitian (skew-hermitian) solution
• re-nonnegative (re-positive) definite solution
• re-nonnegative (re-positive) definite least-rank solution