ON SOLUTIONS TO MATRIX INEQUALITIES WITH APPLICATIONS

Abstract

In this paper, we first study the solution to linear matrix inequality $AXB+(AXB)^* \geqslant (\gt ,\;\leqslant,\;\lt )\;C$ when the matrix $G = (A \quad B^*)$ is full row rank, where $C$ is a Hermitian matrix. Furthermore, for the applications, we derive the representations for the Re-nnd $\{1,2,i\}$-inverses for $A$, $i=3,4$, and the Re-nnd solution to $AXB=C$, some special matrix equations are also considered.