The reflexive and anti-reflexive solutions of the matrix equation A(H) X B=C star

摘要

In this paper, the necessary and sufficient conditions for the solvability of matrix equation AHXB = C over the reflexive or anti-reflexive matrices are given, and the general expression of the solution for a solvable case is obtained. Moreover, the relative optimal approximation problem is considered. The explicit expressions of the optimal approximation solution and the minimum norm solution are both provided. (c) 2006 Published by Elsevier B.V.