Inverse probles of matricem have been widely used in fields of structure design and automatic control .By using the singular value decomposition (SVD)and Moore-Penrose inverse of matrices, this paper establishes the necessary and sufficient conditions for the existence of and the expressions for the anti-symmetric solutions of inverse problem of the matrix equation AX = B under a submatrix constraint. In addition, in the solution set of corresponding problem, the expression of the optimal approximation solution to a given matrix is derived,and a numerical algorithm and a numerical example for ...
