A novel neural network approach for computing eigen-pairs of real antisymmetric matrices

In the present paper, we focus on the problem how to compute all eigen-pairs of any real antisymmetric matrix by the conventional neural network approach without modification the original structure of the neural network. Given any n-dimensional real antisymmetric matrix, our proposed method is based on a n-dimensional ODEs and the preprocessing become comparatively easy. The contributions of this paper are mainly come from two aspects, on the one hand, we constructed the eigen-pairs relationship between those of symmetric matrix and anti-symmetric matrix; on the other hand, we presented a simple method to compute all eigen-pairs of any antisymmetric matrix. Simulations verify the computational capability of the proposed method.