Solvability conditions for algebra inverse eigenvalue problem over set of anti-Hermitian generalized anti-Hamiltonian matrices

By using the characteristic properties of the anti-Hermitian generalized anti-Hamiltonian matrices, we prove some necessary and sufficient conditions of the solvability for algebra inverse eigenvalue problem of anti-Hermitian generalized anti-Hamiltonian matrices, and obtain a general expression of the solution to this problem. By using the properties of the orthogonal projection matrix, we also obtain the expression of the solution to optimal approximate problem of an n×n complex matrix under spectral restriction. Foundation item: Project(10171031) supported by the National Natural Science Foundation of China