The Re-nnd solutions of the matrix equation AxB = C with reference to indefinite inner product

Abstract

In this paper, we first consider the matrix equation AXA[?] = C , where A ? Cn×m, C ? Cn×n and establish necessary and sufficient conditions for the existence of Re-nnd solutions. Further, we determine the necessary and sufficient conditions for the existence of Re-nnd solutions of the equation AXB=C.