The Anti-Symmetric Orthogonal Anti-Symmetric Solution of a Linear Matrix Equation and its Optimal Approximation

This paper defines a new type of matrix, i.e. anti-symmetric orthogonal anti-symmetric matrix, and studies the existence of the solution of this matrix and its optimal approximation in a typical kind of linear matrix equation.By applying the generalized singular value decomposition of matrices , we have established the necessary and sufficient conditions for the existence of solution and the general expression of the solution to this matrix, and have derived the optimal approximation of the solution in the solution set of given matrix.