Procrustes problem for the inverse eigenvalue problem of normal (skew) J-Hamiltonian matrices and normal J-symplectic matrices

A square complex matrix A is called (skew) J-Hamiltonian if AJ is (skew) Hermitian where J is a real normal matrix such that J2 = −I, where I is the identity matrix. In this paper, we solve the Procrustes problem to find normal (skew) J-Hamiltonian solutions for the inverse eigenvalue problem. In addition, a similar problem is investigated for normal J-symplectic matrices.