On Anti-centro-symmetric Solutions of Quaternion Matrix Equation AXA ∗ = B

By means of quaternion generalized singular value decomposition of quaternion matrices, this paper derives necessary and sufficient conditions that quaternion matrix equation AXA ∗ = B has an anti-centrosymmetric solution, and obtains a general expression of the anti-centrosymmetric solutions. In addition, an expression of the optimal approximation solution to a given matrix is derived. Mathematics Subject Classification: 15A24