Let J ∈ ℝn×n be a normal matrix such that J2 = −In, where In is an n-by-n identity matrix. In (S. Gigola, L. Lebtahi, N. Thome in Appl. Math. Lett. 48:36–40, ) it was introduced that a matrix A ∈ ℂn×n is referred to as normal J-Hamiltonian if and only if (AJ)∗ = AJ and AA∗ = A∗A. 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.
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机译：令J∈ℝ n×n 是一个正规矩阵，使得J 2 = −In，其中In是一个n×n的恒等矩阵。在（Appl。Math。Lett。48：36-40，S. Gigola，L.Lebtahi，N.Thome）中，引入了矩阵A∈ℂ n×n 称为当且仅当（AJ） ∗ = A J 和 A A < / em> * = A ∗ A 。此外，给出了此类矩阵反特征值问题可解的充要条件。对于正常偏斜 J -Hamiltonian矩阵，我们提供了上述论文中给出的替代条件。通过使用Moore-Penrose广义逆和广义奇异值分解，获得了其可解性的充要条件，并给出了可解的一般表示。
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