A class of constrained inverse eigenproblem and associated approximation problem for skew symmetric and centrosymmetric matrices

In this paper, a class of constrained inverse eigenproblem and associated approximation problem for skew symmetric and centrosymmetric matrices are essentially decomposed into the same kind subproblems for real antisymmetric matrices with smaller dimensions. We present the general solution of the constrained inverse eigenproblem for skew symmetric and centrosymmetric matrices in real number field. In addition, in corresponding solution set of the constrained inverse eigenproblem for skew symmetric and centrosymmetric matrices, the explicit expression of the nearest matrix to a given matrix in the Frobenius norm is obtained.