Special Matrices And Matrix Equation Problem On Special Matrices

In this paper,we study some classes of special matrices, and discuss several matrix equations on these matrices.In chapter one, we give the definition of the sub-generalized positive definite matrix,study the inverse problem of matix eqution AX = B on the sub-generalized positive definite matrix.In chapter two,we study the necessary and sufficient condition for the solvability of matix equation AXB = Con anti-symmetry matrices, When the solvability holds, the general form of the solution is given, Further more, we study the solvability of matrix equation AXB + CYD = E on anti-symmetry matrices.In chapter three,by the gengeral singular value decomposition of matrix pairs, we get the least-square solution of the following problem:φ = ATXB - BTXTA - D = min...