The solvability conditions for the inverse eigenvalue problem of normal skew J-Hamiltonian matrices

Let [Formula: see text] be a normal matrix such that [Formula: see text], where [Formula: see text] is an n-by-n identity matrix. In (S. Gigola, L. Lebtahi, N. Thome in Appl. Math. Lett. 48:36-40, 2015) it was introduced that a matrix [Formula: see text] is referred to as normal J-Hamiltonian if and only if [Formula: see text] and [Formula: see text]. Furthermore, the necessary and sufficient conditions for the inverse eigenvalue problem of such matrices to be solvable were given. We present some alternative conditions to those given in the aforementioned paper for normal skew J-Hamiltonian matrices. By using Moore-Penrose generalized inverse and generalized singular value decomposition, the necessary and sufficient conditions of its solvability are obtained and a solvable general representation is presented.