The Inverse Problem of Generalized Symmetric and Anti-symmetric Matrix
This paper two kinds of generalized symmetric and anti-symmetric matrix sets are defined. By applying the Moore-Penrose generalized inverse and the decomposition of generalized singular value of matrices, the necessary and sufficient condition for the inverse problem AX=B have a solution in given matrix sets are derived. And the general expression for the solution of the problem are also given.
Keywords: generalized symmetric matrix; generalized anti-symmetric matrix; the decomposition of generalized singular value; optimal approximation; inverse problem