The Inverse Problems Of Matrices Equation A~HXA=B

This paper mainly discusses the following problems:Where S_E is the solution set to Problemâ… orâ…¡a nd (?) is Frobenius norm.When S is all anti-Bihermitian matrices net or is anti-Hermitian generalized Hamilton matrices net, the main results of this paper are as follow:1. The existence of solutions for Problemâ… being proved, the general expression of solutions for Problemâ… is given. When there exist solutions to Problemâ… , the uniqueness of solutions to Problemâ…¢will be found, where S_E is the solution set to Problemâ… .2. After discussion the existence of solution to Problemâ…¡, the expression of Problemâ…¡and the uniqueness of solution for Problemâ…¢will be given, where S_E is the solution set to Problemâ…¡.3. On the linear manifold, the general expression of solution for Problemâ…¡is obtained.